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August 2022
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Intro Stats / AP Statistics Q&A Archive of August 9, 2022

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August 9 of 2022

Multiple Choice How many different license plates are possible if two digits are followed by three letters? 98,876,450 1,404,000 1,757,600 12,647,200

Simplify. Explain your answer: b C n + 1 n - 1

21. In a town fiesta singing competition with 12 contestants, in how many ways can the organizer award the top 3 winners?

Example: Calculate the number of combinations there are of distinct objects taken M at a time.

(c) Use Fermat little theorem to show that (a + b)P = aP + bp mod p for every odd prime p and any positive integer

Which of the following can best define a combination? It is a counting technique where the order of elements is individually counted. It is a counting technique where the order of elements matters. It is a counting technique that considers all possible outcomes when the order of elements is not…

Task 1: Answer each permutation problem completely 1 Find the number of permutations of the letters of the word EVEN. 2 Find the number of permutations of the letters of the word STATISTICS? 3. In how many ways can 3 people be seated around a circular table? In how many ways can 4 people be…

Problem 1. In how many ways can 5 finalist be chosen from 20 contestants?

Activity 3: Using combination notation in solving each of the following problems: 1. How many combinations of three letters can be made from the letters B, E, A, U, T, and Y?

24. Evaluate; Z Bz 3 Pz

5. Find the number of distinguishable permutations of the letters from the word SPOON: 4! = 24 6. In how many ways can 6 people be seated around a circular table given that two of them are insisting to sit beside each other? A 720 B 120 C 48 D 24

Evaluate 5,040, 120, 2,520, and 4,536 numerals can be obtained using the digits 1, 2, 3, 4, 5, and 6. There are many different ten-digit distinguishable permutations of the letters of the word "AZOATIHAN". Find the number of distinguishable permutations.

Text: Read and analyze the following problems carefully. Show your complete solutions. How many V coaches can choose players for the team? Set of # volleyball matches. Write MC members. Publishing company has male and 8 female qualified applicants. If there are 6 available positions, in how…

How many ways can all 4 men and 6 women be arranged in a row if the men must be together? Instruction: Give your answer with NUMERAL only: Do not spell:

C. Evaluate: Solve for the unknown 1. C(10,5) = 252 2. C(12, 2) = 66 3. C(15, r) = 455 4. C(n,3) = 35 5. C (18, r) = 18564

3. Evaluate the coefficients of $x^3$ and $x^4$ in the binomial expansion of $(\frac{x}{3} - 3)^7$. Hence evaluate the coefficient of $x^5$ in the expansion of $(\frac{x}{3} - 3)^7 (x + 6)$.

Abby chose her three ice cream scoops. If ice cream is served in a cone, in how many ways can she choose the ice cream scoops if there are 6 available flavors? How many three-digit numbers can be formed using the digits 6, 7, and 8 without repetition? How many different committees of 5 people…

12.5. 413! 43151 II Evaluate the following permutations. 11. Pz 13. sPe 15. Isp 17. gPo" IP= 19. 2 8P ~OPz 420- 8P 12. 7P3 14. Ps 16. P," &P4 18. ,Pz " 7P6

ACTIVITY NO. 2: Answer each permutation problem completely. How many distinguishable permutations are possible with all the letters of the word ELLIPSES? In how many ways can 12 people occupy the 12 seats in a front row of a mini theatre? How many distinguishable permutations are possible with…

3) Find the number Of ways you can pick and arrange 4 letters from the word GAMERS

4.3 Permutations With Some Identical Balls Refer to the Key '#t7 and solve the problem. How many different ten-digit telephone numbers contain four 7's?

Find the number of permutations of the letters of the word MATHEMATICS. Solution: n! / pqr

If C(of)-120, what is the possible value of D I0? How many live gin be at Aril #appine station of boies Manno Joirns aJ ribbon - cokn #TJppd? 34 3877 107 Zu

Nick took a 10-question quiz in US History in Mr. McCarrol's class. There were 6 true/false (T/F) questions and multiple-choice questions (A, B, C, D, E). How many ways could he answer the T/F and multiple-choice questions? Show your work below:

Find the number of permutations: Type the NUMBER ONLY of your answer: Permutations To find the number of permutations of items chosen at a time, YOU can use the formula nPr where 0 < r < n - (n - r)! / (n - r)! = 52! / (52 - 5)! = 52! / 47! = 52 * 51 * 50 * 49 * 48 =…

How many three-digit positive even integers can be formed from the digits 2, 3,4, 5, 6,and 7 if repetitions of digits are not allowed?

27. In how many ways can 8 people be seated around a circular table if 2 of them insist on sitting beside each other? A. 5040 B. 1544 C. 1454 D. 1440 28. Brian was able to calculate the total number of 3-digit numbers that can be formed from a given set of non-zero digits, without…

Example 3. How many distinguishable signals can be formed displaying eleven flags if 3 of the flags are red, 5 are green, 2 are yellow and 1 is white? Solution: P = 11! / (3! * 5! * 2! * 1!) = 27,720 Thus, there are 27,720 signals that can be formed. ACTIVITY: Find the quotient of the…

In how many ways can three identical issues of a Mathematics magazine, two identical Statistics magazines, and four identical Science magazines be put in a stack? 362,880 40,320 1,728 1,260

An ice cream store offers seven different flavors of ice cream. Find the number of arrangements of three different scoops of ice cream on a cone. The board has 10 members. In how many ways can you representatives be chosen? Shenlie is asked by Jewel to answer four questions: "How many ways can…

A box contains red_ green and yellow balls. In how many ways can balls be chosen such that they are of different colors?

5. What is the value of C(11,11)? A. 0 B. 1 C 10 D. 11

Directions: Define and write the formula for the following, and give examples: Permutation Distinguishable Permutation Circular Permutation

Question Select your answer. A new license plate numbering system has been devised According to this system, each license plate consists of two letters chosen from A B,and C; and two digits chosen from 1,2,3,4, 5,and 6.All letters must be adjacent to each other; and all digits must also be…

What is the numerical value of P(9,5)Â² = 126?

How many arrangements can be formed with the letters of the words: MATH, Business, Philosophical, ORANGE, Biology, MATHEMATICS, Conference, Choice, Sleepless, Combinatorics.

The first ten letters of the English alphabet are to be used by a certain company's 25 employee codes in sets of five. Find the number of combinations: A) 25 B) 225 C) 252 D) 552.

Task #8: Compute the following combinations. "C2", "ZC3", "IC10", "3C5", "5", "25C0" Task #9: Find the number of combinations of the letters of the word CAREFUL taken 2 letters at a time, taken 3 letters at a time, taken 4 letters at a time, taken 5 letters at a time, taken 6 letters at a…

In â‚¬ (9.5) = 126. Which of the following denotes the number of possible selections? cannot be determined

Tiot A) 6 B) 24 the program by How many ways can she arrange 5. A pianist plans to play 5 pieces at a recital. Playing these pieces in different orders? C) 25 D) 3125 A) 120 B) 32 assuming there is no race with 10 runners be completed, 6_ In how many different ways can tie? D) 362,880 B) 1024…

SUPPLs? Qu Want to find the number of permutations of similar Math books, similar English books, and similar Science books in Fort Juhuch. Which of the following expressions will give the answer? P 13t3t? F" 4uz

I. Exercises: Each situation involves a permutation or combination. Determine whether the answer is on a separate sheet of paper. 1. A seating arrangement in a classroom chosen from 5 boys and 6 girls. 2. A team of 2 boys and 3 girls. 3. Selecting the officers of an association.

Determining the top three students of grade 10 students in honors from the batch with you in a party. Selecting to attend together. Choosing three of your classmates to solve the problems below. Write your solution on a separate sheet of paper. 6, and r, what is the number of combinations? 6 If…

How many different permutations are there of n objects taken r at a time? A) nPr B) (n - r)Pr C) (n - 1)Pr

4) lo hox mary ways can you Place + different Look $ On shelf_there Is space_only For three Books

A. 7/3 10. B. 41 If P(n,3) C. 120 = 1716, what is n? 12: ~ ~ B. 13 C. 14 SOLVE THE FOLLOWING PROBLEMS. SHOW YOUR SOLUTIONS: D. 210 D. 15

How many ways can students be seated at a round table? 720 420 320

Let's Practice Solve for the unknown in each number: Write your answer on a separate sheet of paper. Write your complete solution. Given n = 9 and r = 5, find the number of combinations of objects c(n,2) = 21. C(11,5) = _ Results: c(9,t) = 84 C(12,7) = 5.

How many 3-letter words with or without meaning can be formed out of the letters of the word 'LOGARITHMS', if repetition of letters is not allowed? 5040 B. 720 420

12. Count how many ways can 8 students be seated in a row of 4 chairs? 336, 1680, 6720.

be seated in a classroom if there are 7 In how many ways can 4 students available seats? 3150 a 315 5760 b 840

3. A bowl contains 4 red marbles, 5 yellow marbles, and 6 blue marbles. In how many ways can 4 balls be selected given each condition? a. all are yellow b. 1 red, 3 blue c. exactly 2 red

LEARNING ACTIVITY Directions: 1. Solve problems involving permutations. Find the number of ways to arrange couples who want to have their pictures taken, while following health protocols from COVID-19 (wearing face masks, face shields, and practicing social distancing). The couples must…

22. How many 4-digit numbers can be formed from the digits 1, 3, 5, 6, and 8 if no repetition is allowed? A. Combination B. Permutation C. Both D. Cannot be determined

Which of the following expressions is equivalent to C(n, r)? (-lrl (n-T)rl (n-D) 5"'3" Je [U9 9)i" (1^ `. ' 3 D. (n-r)i

14. Which of the following expressions represents the number of distinguishable permutations of the letters of the word ACCOMMODATION? a. 131 b. 12! c. 21312121 d. 2121212! 15. If P = (8, r) = 1,680, what is r? a. 2 b. 3 c. 4 d. 5 16. If P(9, r) = 504, what is r? a. 3 b. 5 c. 6 d.…

A restaurant offers four appetizers, nine entrees, and three desserts. How many different ways can John choose a three course meal? 27 36 100 108

It is done for you as you suggest. Each suit can be formed from a different set of 6 cards. How many cards are in a deck of 52 cards? Each suit has a standard Trigonometry Domain.

In how many ways can they elect among themselves the top positions (President, Vice-president, and others) after the 12 members are chosen? P(12,7) = 3,991,680.

7. In how many ways can 6 math books and 4 science books be arranged ona shelf if there are no restrictions? 3,628,800 36,288 362,880 36,288,000

Learning Task 3.2 Problem Solving Solve each problem completely. Show your solution: From a list of 12 books, how many groups of books can be selected? How many baseball teams of members can be formed from 14 players? From a class of 32 girls and 18 boys, how many study groups of 3 girls and 2…

Which statement illustrates combination? The student body of 10 students wants to elect = a president, vice-president, secretary and treasurer: 5 out of 13 students will ride in 2 car instead ofa van There are 15 applicants for four jobs: computer programmer, software tester, manager and…

Hey everyone! How many contestants are there? What are the 2nd and 3rd place prizes among eight?

LEARNING TASK % Which of the following situations shows combinations? Your answer sheet; Mark COMBINATION if the statement does not require order and write PERMUTATION if the situation requires order. 1. Determining the top three winners in a Science Quiz Bee 2. Forming lines from six given…

Worksheet A lock contains 3 dials, each with ten digits. How many possible sequences of numbers exist? Four students are to be chosen from group of 10 to fill the positions of president_ vice-president, treasurer and secretary: In how many ways can this be accomplished? How many ways can the…

ways B. 12 ways C.36 ways D. 144 ways In how many ways can & committee of 7 students be chosen from 9 juniors and 9 seniors if there must be 4 seniors in the committee? 10,584 ways B. 1,764 ways C.210 Which of the followino ways D. 84 ways

C List & the possible combinations of the following: 11. Alma (A), Ben (B), Carla (C), Daryl (D), Edna (E) taken three at a time 12. The numbers 5, 6, 7, 8, 9 taken two at a time 13. The symbols @, #, %, and 8 taken three at a time

The number of 7-letter arrangements using the word ABSOLUTE is 6720. Demonstrate two ways that this value can be determined. (1 mark) b) Determine the number of arrangements if all the letters of the word REIMANNIAN, if the arrangement must begin with an N. (2 marks)

A declamation contest has 13 participants. In how many ways will the 1st, 2nd, and 3rd winners be selected? A. 227,020,800 B. 5,418 C. 1,716 D. 39

In how many ways can 10 books be arranged on a shelf? How many distinct permutations can be made from the letters of the word MAMAMAYAN? How many ways can you arrange 10 books on a bookshelf that has space for only books? A key ring holds 10 keys. In how many different ways can the…

How many different ways can club choose committee of from 15 members? 32,760 01,365 0 24

Use the following information to answer this question. In Canada, all postal codes have characters in the pattern letter-digit-letter-digit-letter-digit. The first letter of the postal code identifies a specific region. Each of the postal code letters can be any of the 20 letters, and each of…

3) How many ways can you rearrange the letters in the word CHAMPION if there are no restrictions? [K] 6) If the last letter must be N? [A-12] c) If the M and P must be side by side (together)? [A/3] d) If you were making letter arrangements out of the word? [AK3]

Direction: List down the possible outcomes and favorable outcomes of the following: Cathy works in a toy factory. She receives black pants and a red t-shirt or a blue t-shirt and brown pants as her uniform. How many combinations of uniforms does Cathy have? Possible Outcomes: - Black pants and…

The binomial expansion of (2x-3)^(2n-1) has 16 terms. The value of n is 15.

Determine the number of different 3-person or 4-person committees that can be formed from the 8 grade eleven students and the 7 grade 12 students.

In a particular town, all of the streets run north-south or east-west. If a student must travel 7 blocks east and 8 blocks north to arrive at school, assuming her path is always towards the school, the number of different routes that the student can take to get to the school is

A bag contains 6 yellow, 5 white and 7 red books. 5 books are to be chosen randomly without replacement. How many ways can you choose: i. 3 yellow and 2 red books? ii. Books of the same color only?

An ice cream vendor sells 5 flavors of ice cream. You have enough money to sample 2 different flavors. How many different sampling sets could you try? (Hint: there are many ways to figure this out! You could list the sample space, draw a tree diagram...) There would be ways to pick two…

Male student, female student; parent; and school board Lewis Middle School is going to select committee. The committee will have faculty member; member. Here are the positions and the people interested in each: Position People Interested Faculty member Mrs. James, Mr.…

Analyze and solve the following problems. In how many ways can 5 boys and 6 girls be seated in a row of 6 chairs with equal number of boys and girls such that all boys and all girls are together?

Four students, Aisha, Katherine, Natalie, and Gabriella, line up one behind the other. How many different ways can they stand in line?

17 Use the Binomial Theorem to expand the following: (c) (1 + Vw)+

How many ways can 6 adults and 6 children be seated at a round table if 4 particular children insist of sitting together?

Which of the following is equivalent to 5! 120 150

3. How many permutations are there for the letters the word MATH? a. 12 b. 20 c. 22 d.24

Bobby applied for a landline phone in his new house. He was given the number 7-630-8380. How many distinguishable permutations are there in his telephone number?

Practice Exercises Solve the following permutation problems; T A teacher wants to assign different tasks to her 4 students_ In how many possible ways can she do it? 2_ How many distinguishable permutations are possible with all the letters of the word ELLIPSES? 3_ Find the number of different…

3. Evaluate the expression 41 a. 4 D. 12 C.24

Which of the following could be the equation for the number of combinations of n objects taken r at a time? A. C(n,r) = C. C(n,r) B. C(n,r) = D. C(n,r) C. C(n,r) = Tl(n-r)

In how many ways can three runners line up on the starting line? How many ways can books be arranged? Sheln Two different arrangements of objects where some of them are identical are called distinguishable permutations, circular permutations, unique combinations, and circular combinations. Find…

I. In your notebook, illustrate permutations. Situations which of the following make salad selection (units - 10 numbers to homes). Beginning to keep to choose to do after classes. Cooking household. To hang in the walls of your room. Selecting posters. Cubic Root of A: 40310 C. 990 D - B.…

201 P(20,2) = (20 ~ 2)! 20! = 3 (18) !

44 + 2 + 3. (7 - 1)! * 21 / 4. #Ps 5. wP6 2451 (9-5)1

13_ How many ways can eight unique beads be arranged on a chain with clasp? A 40,320 B. 20,160 C 5,040 D 2,520

Which of the following refers t0 the number of ways of selecting objects from set when Ine order Or Arangement is not impontant? Combination Circular permutation B Permutation Fundamental Counting Principle

How many different 5-letter arrangements are there in the word DIGIT? A. 5 B. 30 C. 60 D. 120 Find the number of distinguishable permutations of the letters of the word PASS A. 4 B. 12 C. 36 D. 144

Find the number of permutations of the letters of the word STATISTICS. Solution: There are 10 letters in the word. Assuming that the letters are distinct, there are P(10,10) = 10 permutations. However, we have to take into consideration that the 3 S's are alike, the 3 T's are alike, and the 2…

JC5 1G, 1C; 7, C 23 C 20 C, 6. C,

040 J20 What Is P(10, 5)? A,20 240 30 240 C. 40 240 D, 50 240

1. The number of permutations - 1. B1 2. BP4 3. uP8 4. 9Pa 5. GPs 6. 10P+ 7. 7Pz 8. sz 1Pz 9. 3Pz 10. Jok 11Pz

"How many ways can 2 Physics books, Mathematics books and 3 arranged on a shelf if all books of the same Chemistry books be together? subject may be arranged in any order but must be

ACTIVITY 2 Direction: Answer each permutation problem completely. 1. A teacher wants to assign 10 different tasks to her 10 students. In how many possible ways can she do it? 2. President Duterte will conduct a press conference. In how many ways can five reporters be arranged in a row if they…

Example 3: A Science Club has 20 members. They wish to elect officers consisting of a president, vice president, a secretary, and a treasurer. How many sets of officers are possible? Given: n = 20, r = 4.

A 11 B. 10 24 If C(12,r) = 792, which of the following is a possible value of r? A 8 B. 7 C. 6 25 A caterer offers 3 kinds of soup, 7 kinds of main dish; 4 kinds of vegetable dish.

There are 7 different rides at an amusement park. You have a ticket that allows you to ride 3 different attractions. In how many different orders can you use the 3 rides in?

. A True or False test consists of 10 qucstions. If all the questions arc answered, in how many different ways Can this b< donc:

Find the distinct permutation of the letters of the word POSSIBLE 40,320 20.160 5040

6. In how many ways can 8 people form circle for a folk dance? 5,400 5,040 5004 4,050 Option 5

How many elements are there if you draw a face card or a blackjack in a standard deck of 52 cards? a) 1 b) 2 c) 4 d) 12

Permutation of n taken r = n! / (n-r)! Circular Permutation

How many ways can 10 people fall in line if a certain 2 refuse to be parted? 10! (104)(24) (91)(24) 91

Ways to Calculate Sil Wiliiuul Ejuiclui A 14,400 B. 10,000 C. 3,628,800 D. 362,811. Find the number of distinguishable permutations of the digits of the number 1,412,233. B. 008 C. 402 D. 42 A. 630.

List all the 3-digit numbers that can be created by rearranging these number tiles. 4 8

Time lelt 0.5439 Find the number of distinguishable permutations of the letters in the word MATHEMATICS Ata

Find the number of distinguishable permutations Of the digits of the number 234 424. 720 c. 12

3. In a group of 7 boys and 5 girls , how many ways can they be arranged in a line if seven f them will be seated in & row?

What is C(15, = 5005 ? (Write only 1 possible answer)

How do you determine if a situation or problem involves permutation and combination? What is permutation? What is combination? What is the difference between permutation and combination?

In how many ways can you arrange 10 different keys on a key ring if three of such rings have to be placed next to each other? Your answer

What is the number of distinguishable permutations of letters in the word ASTRAZENECA? 39,916,800 108,800 3,326,400 652 BUU

Answer each 9. Form a class of 32 girls and 18 boys, how many study groups of 3 girls and 2 boys can be formed?

Solutions in your Answer Sheet 1.1C4 2. 1Cs 3.2eC(4,2)-10 researcher needs 6 people to test the medical COMIDAC.

81 5 P = 312121 P=

Five Grade 10 students are seated around a circular table while dining in a restaurant. In how many ways can they be arranged? 24 120 720

Mutually Inclusive Events: Permutation and Combination Illustration: Permutation and Combination problems 1. Choosing the elements of a subset from a given set. 2. Choosing questions to answer out of 10 questions. 3. Determining the top three winners in a Math Quiz Bee. 4.…

1 Find the number of permutations of the letters of the word MATHEMATICS 2 In how many ways can 3 girls and 3 boys sit around a circular table so that boys and girls alternate?

In how many ways can 6 people be arranged to stand (a) ron? #(b) in 2 rows of 3?

Find the number of permutation of the letter of the word ROSE"

11Pz X 121 P120 Simplify 121P1

6. A five-letter code will be formed from the letters of the word KEYBOARD. These are the conditions: If the first letter is vowel, then the second letter must be K and the last letter must be a vowel as well: If the first letter is consonant; the second letter must consonant and the last…

In a 15-item Mathematics problem-solving test, how many ways can you select 5 problems to solve? A. 3,003 B. 360,360 C. 1,365 D. 2,002

What is 0.120? b: 720, C: 5040, d: 40,320

A committee of three men and four women is to be selected from six men and seven women. Find the number of ways in which such a committee can be formed.

Corazon's Eatery has 5 different sandwiches, with 2 choices of potato chips, 3 types of salad and 8 different beverages. How many different lunch combinations consisting of a sandwich, chips, salad, and beverage can be ordered? 17 270 240 18

Given the expression (4x^2y), using the Binomial Theorem: a) State the number of terms of the expansion. b) Find the fifth term of the expansion. c) Find the coefficient of x^2y^21.

There are twelve horses in competition. The top three winning horses will receive a cash prize. How many possible winning orders are there in the competition?

A project manager has 9 engineers in her team, 4 men and 5 women. How many committees of size 3 are possible with no restrictions? How many committees have 1 man and 2 women? How many committees have at most 2 women? How many committees have at least 2 men?

5,040 D; odd numbers 1-9? be formed using the How many three-digit numbers can C. 756 252 D. 2,288 504 third, and fourth place on - first, second, 5.

Find the numerical coefficient of the term involving x 3 y 2 in the expansion (4x 2y -3z)^5

Four items are selected from a group of 7. Which of the following calculations is incorrect? 0z Oza Onz6*5*4

JON Question 20 Not yet answered Find Ihe coofficiont of Iho X4 term in Ihe expansion of 10 Marked out 0( x2 2x Ix) Aie 20 Flag' question Select one: A 15 B. 120 C.240 D. 60 E.30 Next

3) 2"d term in expansion of (1+3y)

Find the 6th term of the binomial expansion: (xy)^10.

Consider the expansion of x(2x^2 + a/x)^7. The constant term is 20412. Find a.

Fifteen teams play in the Eastern Conference of the NBA. How many ways can the teams finish 1st, 2nd, 3rd, 4th, 5th, 6th, 7th, and 8th?

Assume that each of the n trials is independent and that p is the probability of success on a given trial. Use the binomial probability formula to find P(x): n = 19, X = 2, p =

Use the Binomial Theorem to find the coefficient of in the expansion of (x + 1)^10. The coefficient of

An employee consists of 17 men and 12 women. How many ways can this employee choose a committee of 3 men?

CURRENT OBJECTIVE: Find the number of combinations using the formula. Question: How many different exercise song combinations are possible if Cowaro can choose songs during his workout from a selection of 11 songs? Provide your desired number.

In how many ways can you answer a 15-question test if you answer each question with either "false" or "always false"? 100, 15 105, 25 None

There are 52 runners in a race How many ways can the runners finish first, second, and third? There are different ways that the runners can finish first through third (Type a whole number )

Evaluate 48C5 using technology or the formula

ANSWER FIVE QUESTIONS ONLY 94. UI SLJa & ISJIY 841 UIBIQO (e)l expansion of (2+x)

How can I calculate the average income? What is the average income of an individual?

The population standard deviation for the heights of dogs, in inches, in a city is 3.7 inches. If we want to be 95% confident that the sample mean is within 2 inches of the true population mean, what is the minimum sample size that can be taken?

The value zc is a value from the standard normal distribution such that P -zc x zc 5 c. 2. Statistical Literacy The point estimate

Find class boundaries, midpoint, and width for the class 123-143

A reading specialist in a large public school system believes that the more time students spend reading, the better they will do in school. She plans a middle school experiment in which an SRS of 30 eighth graders will be assigned four extra hours of reading per week, an SRS of 30 seventh…

The mean thrust of a certain model jet engine is 9500 pounds. Concerned that a production process change might have lowered the thrust, an inspector tests a sample of units, calculating a mean of 9350 pounds with a z-score of -2.46 and a P-value of 0.0069. Which of the following is the most…

All of the following statements are true for all discrete random variables except for which one? A. The possible outcomes must all be numerical. B. The possible outcomes must be mutually exclusive. C. The mean (expected value) always equals the sum of the products obtained by multiplying…

Given that the sample has a standard deviation of zero, which of the following is a true statement? A. The standard deviation of the population is also zero. B. The sample mean and sample median are equal. C. The sample may have outliers. D. The population has a symmetric…

Data are collected on income levels x versus number of bank accounts y. Summary calculations give = 32,000; sx = 11,500; = 1.7; sy = 0.4, and r = 0.42. What is the slope of the least squares regression line of number of bank accounts on income level?

It is estimated that 30% of all cars parked in a metered lot outside City Hall receive tickets for meter violations. In a random sample of 5 cars parked in this lot, what is the probability that at least one receives a parking ticket? A. 1 - (0.3)5 B. 1 - (0.7)5 C. 5(0.3)(0.7)4 D. 5(0.3)4…

A survey was conducted to determine the percentage of parents who would support raising the legal driving age to 18. The results were stated as 67% with a margin of error of ±3%. What is meant by ±3%? A. Three percent of the population were not surveyed. B. In the sample, the percentage of…

Leech therapy is used in traditional medicine for treating localized pain. In a double blind experiment on 50 patients with osteoarthritis of the knee, half are randomly selected to receive injections of leech saliva while the rest receive a placebo. Pain levels 7 days later among those…

Random samples of size n are drawn from a population. The mean of each sample is calculated, and the standard deviation of this set of sample means is found. Then the procedure is repeated, this time with samples of size 4n. How does the standard deviation of the second group compare with the…

We are interested in the proportion p of people who are unemployed in a large city. Eight percent of a simple random sample of 500 people are unemployed. What is the midpoint for a 95% confidence interval estimate of p? A. 0.012 B. 0.025 C. 0.475 D. p E. None of the above.

Suppose that 54% of the graduates from your high school go on to 4-year colleges, 20% go on to 2-year colleges, 19% find employment, and the remaining 7% search for a job. If a randomly selected student is not going on to a 2-year college, what is the probability she will be going on to a…

For their first exam, students in an AP Statistics class studied an average of 4 hours with a standard deviation of 1 hour. Almost everyone did poorly on the exam, and so for the second exam every student studied 10 hours. What is the correlation between the numbers of hours students studied…

The waiting times for a new roller coaster ride are normally distributed with a mean of 35 minutes and a standard deviation of 10 minutes. If there are 150,000 riders the first summer, which of the following is the shortest time interval associated with 100,000 riders? A. 0 to 31.7…

To test whether extensive exercise lowers the resting heart rate, a study is performed by randomly selecting half of a group of volunteers to exercise 1 hour each morning, while the rest are instructed to perform no exercise. Is this study an experiment or an observational study? A. An…

Suppose P(X) = 0.35 and P(Y) = 0.40. If P(X|Y) = 0.28, what is P(Y|X)?

A company has a choice of three investment schemes. Option I gives a sure $25,000 return on investment. Option II gives a 50% chance of returning $50,000 and a 50% chance of returning $10,000. Option III gives a 5% chance of returning $100,000 and a 95% chance of returning nothing. Which option…

Two commercial flights per day are made from a small county airport. The airport manager tabulates the number of on-time departures for a sample of 200 days. What is the χ2 statistic for a goodness-of-fit test that the distribution is binomial with probability equal to 0.8 that a flight…

From a group of 35 people, you have to choose 15 people for a sports team. How many different ways can you choose a group of this many people?

From a group of 35 people, you have to choose 21 people for a sports team. How many different ways can you choose a group of this many people?

From a group of 35 people, you have to choose 13 people for a sports team. How many different ways can you choose a group of this many people?

From a group of 35 people, you have to choose 12 people for a sports team. How many different ways can you choose a group of this many people?

From a group of 35 people, you have to choose 23 people for a sports team. How many different ways can you choose a group of this many people?

Find the inter quartile range of the following data set: 11, 23, 46, 65, 74, 98, 101

Find the inter quartile range of the following data set: 14, 54, 62, 65, 84, 91, 101

Find the inter quartile range of the following data set: 3, 4, 5, 19, 20, 21

Find the inter quartile range of the following data set: 103, 105, 107, 109, 111, 113

Find the inter quartile range of the following data set: 34, 64, 90, 165, 189, 200

A sample of 93 students has a mean weight of 41 kg. Find the Z score of a sample from a population with a mean weight of 79 kg and a standard deviation of 40 kg.

A sample of 78 students has a mean weight of 49 kg. Find the Z score of a sample from a population with a mean weight of 65 kg and a standard deviation of 92 kg.

A sample of 53 students has a mean weight of 30 kg. Find the Z score of a sample from a population with a mean weight of 92 kg and a standard deviation of 60 kg.

A sample of 59 students has a mean weight of 97 kg. Find the Z score of a sample from a population with a mean weight of 36 kg and a standard deviation of 65 kg.

A sample of 85 students has a mean weight of 85 kg. Find the Z score of a sample from a population with a mean weight of 33 kg and a standard deviation of 93 kg.

Explain what the mean is, the formula and calculate it for the following set of numbers: 72, 18, 77, 75, 82

Explain what the mean is, the formula and calculate it for the following set of numbers: 46, 13, 61, 89, 87

Explain what the mean is, the formula and calculate it for the following set of numbers: 43, 1, 87, 34, 24

Explain what the mean is, the formula and calculate it for the following set of numbers: 70, 45, 3, 99, 33

Explain what the mean is, the formula and calculate it for the following set of numbers: 96, 9, 56, 37, 46

82 students enter a contest at school. The contest offers a first, second, and third prize. How many different combinations of 1st, 2nd, and 3rd place winners can there be?

71 students enter a contest at school. The contest offers a first, second, and third prize. How many different combinations of 1st, 2nd, and 3rd place winners can there be?

52 students enter a contest at school. The contest offers a first, second, and third prize. How many different combinations of 1st, 2nd, and 3rd place winners can there be?

79 students enter a contest at school. The contest offers a first, second, and third prize. How many different combinations of 1st, 2nd, and 3rd place winners can there be?

Multiple Choice How many different license plates are possible if two digits are followed by three letters? 98,876,450 1,404,000 1,757,600 12,647,200

Simplify. Explain your answer: b C n + 1 n - 1

21. In a town fiesta singing competition with 12 contestants, in how many ways can the organizer award the top 3 winners?

Example: Calculate the number of combinations there are of distinct objects taken M at a time.

(c) Use Fermat little theorem to show that (a + b)P = aP + bp mod p for every odd prime p and any positive integer

Which of the following can best define a combination? It is a counting technique where the order of elements is individually counted. It is a counting technique where the order of elements matters. It is a counting technique that considers all possible outcomes when the order of elements is not…

Task 1: Answer each permutation problem completely 1 Find the number of permutations of the letters of the word EVEN. 2 Find the number of permutations of the letters of the word STATISTICS? 3. In how many ways can 3 people be seated around a circular table? In how many ways can 4 people be…

Problem 1. In how many ways can 5 finalist be chosen from 20 contestants?

Activity 3: Using combination notation in solving each of the following problems: 1. How many combinations of three letters can be made from the letters B, E, A, U, T, and Y?

24. Evaluate; Z Bz 3 Pz

5. Find the number of distinguishable permutations of the letters from the word SPOON: 4! = 24 6. In how many ways can 6 people be seated around a circular table given that two of them are insisting to sit beside each other? A 720 B 120 C 48 D 24

Evaluate 5,040, 120, 2,520, and 4,536 numerals can be obtained using the digits 1, 2, 3, 4, 5, and 6. There are many different ten-digit distinguishable permutations of the letters of the word "AZOATIHAN". Find the number of distinguishable permutations.

Text: Read and analyze the following problems carefully. Show your complete solutions. How many V coaches can choose players for the team? Set of # volleyball matches. Write MC members. Publishing company has male and 8 female qualified applicants. If there are 6 available positions, in how…

How many ways can all 4 men and 6 women be arranged in a row if the men must be together? Instruction: Give your answer with NUMERAL only: Do not spell:

C. Evaluate: Solve for the unknown 1. C(10,5) = 252 2. C(12, 2) = 66 3. C(15, r) = 455 4. C(n,3) = 35 5. C (18, r) = 18564

3. Evaluate the coefficients of $x^3$ and $x^4$ in the binomial expansion of $(\frac{x}{3} - 3)^7$. Hence evaluate the coefficient of $x^5$ in the expansion of $(\frac{x}{3} - 3)^7 (x + 6)$.

Abby chose her three ice cream scoops. If ice cream is served in a cone, in how many ways can she choose the ice cream scoops if there are 6 available flavors? How many three-digit numbers can be formed using the digits 6, 7, and 8 without repetition? How many different committees of 5 people…

12.5. 413! 43151 II Evaluate the following permutations. 11. Pz 13. sPe 15. Isp 17. gPo" IP= 19. 2 8P ~OPz 420- 8P 12. 7P3 14. Ps 16. P," &P4 18. ,Pz " 7P6

ACTIVITY NO. 2: Answer each permutation problem completely. How many distinguishable permutations are possible with all the letters of the word ELLIPSES? In how many ways can 12 people occupy the 12 seats in a front row of a mini theatre? How many distinguishable permutations are possible with…

3) Find the number Of ways you can pick and arrange 4 letters from the word GAMERS

4.3 Permutations With Some Identical Balls Refer to the Key '#t7 and solve the problem. How many different ten-digit telephone numbers contain four 7's?

Find the number of permutations of the letters of the word MATHEMATICS. Solution: n! / pqr

If C(of)-120, what is the possible value of D I0? How many live gin be at Aril #appine station of boies Manno Joirns aJ ribbon - cokn #TJppd? 34 3877 107 Zu

Nick took a 10-question quiz in US History in Mr. McCarrol's class. There were 6 true/false (T/F) questions and multiple-choice questions (A, B, C, D, E). How many ways could he answer the T/F and multiple-choice questions? Show your work below:

Find the number of permutations: Type the NUMBER ONLY of your answer: Permutations To find the number of permutations of items chosen at a time, YOU can use the formula nPr where 0 < r < n - (n - r)! / (n - r)! = 52! / (52 - 5)! = 52! / 47! = 52 * 51 * 50 * 49 * 48 =…

How many three-digit positive even integers can be formed from the digits 2, 3,4, 5, 6,and 7 if repetitions of digits are not allowed?

27. In how many ways can 8 people be seated around a circular table if 2 of them insist on sitting beside each other? A. 5040 B. 1544 C. 1454 D. 1440 28. Brian was able to calculate the total number of 3-digit numbers that can be formed from a given set of non-zero digits, without…

Example 3. How many distinguishable signals can be formed displaying eleven flags if 3 of the flags are red, 5 are green, 2 are yellow and 1 is white? Solution: P = 11! / (3! * 5! * 2! * 1!) = 27,720 Thus, there are 27,720 signals that can be formed. ACTIVITY: Find the quotient of the…

In how many ways can three identical issues of a Mathematics magazine, two identical Statistics magazines, and four identical Science magazines be put in a stack? 362,880 40,320 1,728 1,260

An ice cream store offers seven different flavors of ice cream. Find the number of arrangements of three different scoops of ice cream on a cone. The board has 10 members. In how many ways can you representatives be chosen? Shenlie is asked by Jewel to answer four questions: "How many ways can…

A box contains red_ green and yellow balls. In how many ways can balls be chosen such that they are of different colors?

5. What is the value of C(11,11)? A. 0 B. 1 C 10 D. 11

Directions: Define and write the formula for the following, and give examples: Permutation Distinguishable Permutation Circular Permutation

Question Select your answer. A new license plate numbering system has been devised According to this system, each license plate consists of two letters chosen from A B,and C; and two digits chosen from 1,2,3,4, 5,and 6.All letters must be adjacent to each other; and all digits must also be…

What is the numerical value of P(9,5)Â² = 126?

How many arrangements can be formed with the letters of the words: MATH, Business, Philosophical, ORANGE, Biology, MATHEMATICS, Conference, Choice, Sleepless, Combinatorics.

The first ten letters of the English alphabet are to be used by a certain company's 25 employee codes in sets of five. Find the number of combinations: A) 25 B) 225 C) 252 D) 552.

Task #8: Compute the following combinations. "C2", "ZC3", "IC10", "3C5", "5", "25C0" Task #9: Find the number of combinations of the letters of the word CAREFUL taken 2 letters at a time, taken 3 letters at a time, taken 4 letters at a time, taken 5 letters at a time, taken 6 letters at a…

In â‚¬ (9.5) = 126. Which of the following denotes the number of possible selections? cannot be determined

Tiot A) 6 B) 24 the program by How many ways can she arrange 5. A pianist plans to play 5 pieces at a recital. Playing these pieces in different orders? C) 25 D) 3125 A) 120 B) 32 assuming there is no race with 10 runners be completed, 6_ In how many different ways can tie? D) 362,880 B) 1024…

SUPPLs? Qu Want to find the number of permutations of similar Math books, similar English books, and similar Science books in Fort Juhuch. Which of the following expressions will give the answer? P 13t3t? F" 4uz

I. Exercises: Each situation involves a permutation or combination. Determine whether the answer is on a separate sheet of paper. 1. A seating arrangement in a classroom chosen from 5 boys and 6 girls. 2. A team of 2 boys and 3 girls. 3. Selecting the officers of an association.

Determining the top three students of grade 10 students in honors from the batch with you in a party. Selecting to attend together. Choosing three of your classmates to solve the problems below. Write your solution on a separate sheet of paper. 6, and r, what is the number of combinations? 6 If…

How many different permutations are there of n objects taken r at a time? A) nPr B) (n - r)Pr C) (n - 1)Pr

4) lo hox mary ways can you Place + different Look $ On shelf_there Is space_only For three Books

A. 7/3 10. B. 41 If P(n,3) C. 120 = 1716, what is n? 12: ~ ~ B. 13 C. 14 SOLVE THE FOLLOWING PROBLEMS. SHOW YOUR SOLUTIONS: D. 210 D. 15

How many ways can students be seated at a round table? 720 420 320

Let's Practice Solve for the unknown in each number: Write your answer on a separate sheet of paper. Write your complete solution. Given n = 9 and r = 5, find the number of combinations of objects c(n,2) = 21. C(11,5) = _ Results: c(9,t) = 84 C(12,7) = 5.

How many 3-letter words with or without meaning can be formed out of the letters of the word 'LOGARITHMS', if repetition of letters is not allowed? 5040 B. 720 420

12. Count how many ways can 8 students be seated in a row of 4 chairs? 336, 1680, 6720.

be seated in a classroom if there are 7 In how many ways can 4 students available seats? 3150 a 315 5760 b 840

3. A bowl contains 4 red marbles, 5 yellow marbles, and 6 blue marbles. In how many ways can 4 balls be selected given each condition? a. all are yellow b. 1 red, 3 blue c. exactly 2 red

LEARNING ACTIVITY Directions: 1. Solve problems involving permutations. Find the number of ways to arrange couples who want to have their pictures taken, while following health protocols from COVID-19 (wearing face masks, face shields, and practicing social distancing). The couples must…

22. How many 4-digit numbers can be formed from the digits 1, 3, 5, 6, and 8 if no repetition is allowed? A. Combination B. Permutation C. Both D. Cannot be determined

Which of the following expressions is equivalent to C(n, r)? (-lrl (n-T)rl (n-D) 5"'3" Je [U9 9)i" (1^ `. ' 3 D. (n-r)i

14. Which of the following expressions represents the number of distinguishable permutations of the letters of the word ACCOMMODATION? a. 131 b. 12! c. 21312121 d. 2121212! 15. If P = (8, r) = 1,680, what is r? a. 2 b. 3 c. 4 d. 5 16. If P(9, r) = 504, what is r? a. 3 b. 5 c. 6 d.…

A restaurant offers four appetizers, nine entrees, and three desserts. How many different ways can John choose a three course meal? 27 36 100 108

It is done for you as you suggest. Each suit can be formed from a different set of 6 cards. How many cards are in a deck of 52 cards? Each suit has a standard Trigonometry Domain.

In how many ways can they elect among themselves the top positions (President, Vice-president, and others) after the 12 members are chosen? P(12,7) = 3,991,680.

7. In how many ways can 6 math books and 4 science books be arranged ona shelf if there are no restrictions? 3,628,800 36,288 362,880 36,288,000

Learning Task 3.2 Problem Solving Solve each problem completely. Show your solution: From a list of 12 books, how many groups of books can be selected? How many baseball teams of members can be formed from 14 players? From a class of 32 girls and 18 boys, how many study groups of 3 girls and 2…

Which statement illustrates combination? The student body of 10 students wants to elect = a president, vice-president, secretary and treasurer: 5 out of 13 students will ride in 2 car instead ofa van There are 15 applicants for four jobs: computer programmer, software tester, manager and…

Hey everyone! How many contestants are there? What are the 2nd and 3rd place prizes among eight?

LEARNING TASK % Which of the following situations shows combinations? Your answer sheet; Mark COMBINATION if the statement does not require order and write PERMUTATION if the situation requires order. 1. Determining the top three winners in a Science Quiz Bee 2. Forming lines from six given…

Worksheet A lock contains 3 dials, each with ten digits. How many possible sequences of numbers exist? Four students are to be chosen from group of 10 to fill the positions of president_ vice-president, treasurer and secretary: In how many ways can this be accomplished? How many ways can the…

ways B. 12 ways C.36 ways D. 144 ways In how many ways can & committee of 7 students be chosen from 9 juniors and 9 seniors if there must be 4 seniors in the committee? 10,584 ways B. 1,764 ways C.210 Which of the followino ways D. 84 ways

C List & the possible combinations of the following: 11. Alma (A), Ben (B), Carla (C), Daryl (D), Edna (E) taken three at a time 12. The numbers 5, 6, 7, 8, 9 taken two at a time 13. The symbols @, #, %, and 8 taken three at a time

The number of 7-letter arrangements using the word ABSOLUTE is 6720. Demonstrate two ways that this value can be determined. (1 mark) b) Determine the number of arrangements if all the letters of the word REIMANNIAN, if the arrangement must begin with an N. (2 marks)

A declamation contest has 13 participants. In how many ways will the 1st, 2nd, and 3rd winners be selected? A. 227,020,800 B. 5,418 C. 1,716 D. 39

In how many ways can 10 books be arranged on a shelf? How many distinct permutations can be made from the letters of the word MAMAMAYAN? How many ways can you arrange 10 books on a bookshelf that has space for only books? A key ring holds 10 keys. In how many different ways can the…

How many different ways can club choose committee of from 15 members? 32,760 01,365 0 24

Use the following information to answer this question. In Canada, all postal codes have characters in the pattern letter-digit-letter-digit-letter-digit. The first letter of the postal code identifies a specific region. Each of the postal code letters can be any of the 20 letters, and each of…

3) How many ways can you rearrange the letters in the word CHAMPION if there are no restrictions? [K] 6) If the last letter must be N? [A-12] c) If the M and P must be side by side (together)? [A/3] d) If you were making letter arrangements out of the word? [AK3]

Direction: List down the possible outcomes and favorable outcomes of the following: Cathy works in a toy factory. She receives black pants and a red t-shirt or a blue t-shirt and brown pants as her uniform. How many combinations of uniforms does Cathy have? Possible Outcomes: - Black pants and…

The binomial expansion of (2x-3)^(2n-1) has 16 terms. The value of n is 15.

Determine the number of different 3-person or 4-person committees that can be formed from the 8 grade eleven students and the 7 grade 12 students.

In a particular town, all of the streets run north-south or east-west. If a student must travel 7 blocks east and 8 blocks north to arrive at school, assuming her path is always towards the school, the number of different routes that the student can take to get to the school is

A bag contains 6 yellow, 5 white and 7 red books. 5 books are to be chosen randomly without replacement. How many ways can you choose: i. 3 yellow and 2 red books? ii. Books of the same color only?

An ice cream vendor sells 5 flavors of ice cream. You have enough money to sample 2 different flavors. How many different sampling sets could you try? (Hint: there are many ways to figure this out! You could list the sample space, draw a tree diagram...) There would be ways to pick two…

Male student, female student; parent; and school board Lewis Middle School is going to select committee. The committee will have faculty member; member. Here are the positions and the people interested in each: Position People Interested Faculty member Mrs. James, Mr.…

Analyze and solve the following problems. In how many ways can 5 boys and 6 girls be seated in a row of 6 chairs with equal number of boys and girls such that all boys and all girls are together?

Four students, Aisha, Katherine, Natalie, and Gabriella, line up one behind the other. How many different ways can they stand in line?

17 Use the Binomial Theorem to expand the following: (c) (1 + Vw)+

How many ways can 6 adults and 6 children be seated at a round table if 4 particular children insist of sitting together?

Which of the following is equivalent to 5! 120 150

3. How many permutations are there for the letters the word MATH? a. 12 b. 20 c. 22 d.24

Bobby applied for a landline phone in his new house. He was given the number 7-630-8380. How many distinguishable permutations are there in his telephone number?

Practice Exercises Solve the following permutation problems; T A teacher wants to assign different tasks to her 4 students_ In how many possible ways can she do it? 2_ How many distinguishable permutations are possible with all the letters of the word ELLIPSES? 3_ Find the number of different…

3. Evaluate the expression 41 a. 4 D. 12 C.24

Which of the following could be the equation for the number of combinations of n objects taken r at a time? A. C(n,r) = C. C(n,r) B. C(n,r) = D. C(n,r) C. C(n,r) = Tl(n-r)

In how many ways can three runners line up on the starting line? How many ways can books be arranged? Sheln Two different arrangements of objects where some of them are identical are called distinguishable permutations, circular permutations, unique combinations, and circular combinations. Find…

I. In your notebook, illustrate permutations. Situations which of the following make salad selection (units - 10 numbers to homes). Beginning to keep to choose to do after classes. Cooking household. To hang in the walls of your room. Selecting posters. Cubic Root of A: 40310 C. 990 D - B.…

201 P(20,2) = (20 ~ 2)! 20! = 3 (18) !

44 + 2 + 3. (7 - 1)! * 21 / 4. #Ps 5. wP6 2451 (9-5)1

13_ How many ways can eight unique beads be arranged on a chain with clasp? A 40,320 B. 20,160 C 5,040 D 2,520

Which of the following refers t0 the number of ways of selecting objects from set when Ine order Or Arangement is not impontant? Combination Circular permutation B Permutation Fundamental Counting Principle

How many different 5-letter arrangements are there in the word DIGIT? A. 5 B. 30 C. 60 D. 120 Find the number of distinguishable permutations of the letters of the word PASS A. 4 B. 12 C. 36 D. 144

Find the number of permutations of the letters of the word STATISTICS. Solution: There are 10 letters in the word. Assuming that the letters are distinct, there are P(10,10) = 10 permutations. However, we have to take into consideration that the 3 S's are alike, the 3 T's are alike, and the 2…

JC5 1G, 1C; 7, C 23 C 20 C, 6. C,

040 J20 What Is P(10, 5)? A,20 240 30 240 C. 40 240 D, 50 240

1. The number of permutations - 1. B1 2. BP4 3. uP8 4. 9Pa 5. GPs 6. 10P+ 7. 7Pz 8. sz 1Pz 9. 3Pz 10. Jok 11Pz

"How many ways can 2 Physics books, Mathematics books and 3 arranged on a shelf if all books of the same Chemistry books be together? subject may be arranged in any order but must be

ACTIVITY 2 Direction: Answer each permutation problem completely. 1. A teacher wants to assign 10 different tasks to her 10 students. In how many possible ways can she do it? 2. President Duterte will conduct a press conference. In how many ways can five reporters be arranged in a row if they…

Example 3: A Science Club has 20 members. They wish to elect officers consisting of a president, vice president, a secretary, and a treasurer. How many sets of officers are possible? Given: n = 20, r = 4.

A 11 B. 10 24 If C(12,r) = 792, which of the following is a possible value of r? A 8 B. 7 C. 6 25 A caterer offers 3 kinds of soup, 7 kinds of main dish; 4 kinds of vegetable dish.

There are 7 different rides at an amusement park. You have a ticket that allows you to ride 3 different attractions. In how many different orders can you use the 3 rides in?

. A True or False test consists of 10 qucstions. If all the questions arc answered, in how many different ways Can this b< donc:

Find the distinct permutation of the letters of the word POSSIBLE 40,320 20.160 5040

6. In how many ways can 8 people form circle for a folk dance? 5,400 5,040 5004 4,050 Option 5

How many elements are there if you draw a face card or a blackjack in a standard deck of 52 cards? a) 1 b) 2 c) 4 d) 12

Permutation of n taken r = n! / (n-r)! Circular Permutation

How many ways can 10 people fall in line if a certain 2 refuse to be parted? 10! (104)(24) (91)(24) 91

Ways to Calculate Sil Wiliiuul Ejuiclui A 14,400 B. 10,000 C. 3,628,800 D. 362,811. Find the number of distinguishable permutations of the digits of the number 1,412,233. B. 008 C. 402 D. 42 A. 630.

List all the 3-digit numbers that can be created by rearranging these number tiles. 4 8

Time lelt 0.5439 Find the number of distinguishable permutations of the letters in the word MATHEMATICS Ata

Find the number of distinguishable permutations Of the digits of the number 234 424. 720 c. 12

3. In a group of 7 boys and 5 girls , how many ways can they be arranged in a line if seven f them will be seated in & row?

What is C(15, = 5005 ? (Write only 1 possible answer)

How do you determine if a situation or problem involves permutation and combination? What is permutation? What is combination? What is the difference between permutation and combination?

In how many ways can you arrange 10 different keys on a key ring if three of such rings have to be placed next to each other? Your answer

What is the number of distinguishable permutations of letters in the word ASTRAZENECA? 39,916,800 108,800 3,326,400 652 BUU

Answer each 9. Form a class of 32 girls and 18 boys, how many study groups of 3 girls and 2 boys can be formed?

Solutions in your Answer Sheet 1.1C4 2. 1Cs 3.2eC(4,2)-10 researcher needs 6 people to test the medical COMIDAC.

81 5 P = 312121 P=

Five Grade 10 students are seated around a circular table while dining in a restaurant. In how many ways can they be arranged? 24 120 720

Mutually Inclusive Events: Permutation and Combination Illustration: Permutation and Combination problems 1. Choosing the elements of a subset from a given set. 2. Choosing questions to answer out of 10 questions. 3. Determining the top three winners in a Math Quiz Bee. 4.…

1 Find the number of permutations of the letters of the word MATHEMATICS 2 In how many ways can 3 girls and 3 boys sit around a circular table so that boys and girls alternate?

In how many ways can 6 people be arranged to stand (a) ron? #(b) in 2 rows of 3?

Find the number of permutation of the letter of the word ROSE"

11Pz X 121 P120 Simplify 121P1

6. A five-letter code will be formed from the letters of the word KEYBOARD. These are the conditions: If the first letter is vowel, then the second letter must be K and the last letter must be a vowel as well: If the first letter is consonant; the second letter must consonant and the last…

In a 15-item Mathematics problem-solving test, how many ways can you select 5 problems to solve? A. 3,003 B. 360,360 C. 1,365 D. 2,002

What is 0.120? b: 720, C: 5040, d: 40,320

A committee of three men and four women is to be selected from six men and seven women. Find the number of ways in which such a committee can be formed.

Corazon's Eatery has 5 different sandwiches, with 2 choices of potato chips, 3 types of salad and 8 different beverages. How many different lunch combinations consisting of a sandwich, chips, salad, and beverage can be ordered? 17 270 240 18

Given the expression (4x^2y), using the Binomial Theorem: a) State the number of terms of the expansion. b) Find the fifth term of the expansion. c) Find the coefficient of x^2y^21.

There are twelve horses in competition. The top three winning horses will receive a cash prize. How many possible winning orders are there in the competition?

A project manager has 9 engineers in her team, 4 men and 5 women. How many committees of size 3 are possible with no restrictions? How many committees have 1 man and 2 women? How many committees have at most 2 women? How many committees have at least 2 men?

5,040 D; odd numbers 1-9? be formed using the How many three-digit numbers can C. 756 252 D. 2,288 504 third, and fourth place on - first, second, 5.

Find the numerical coefficient of the term involving x 3 y 2 in the expansion (4x 2y -3z)^5

Four items are selected from a group of 7. Which of the following calculations is incorrect? 0z Oza Onz6*5*4

JON Question 20 Not yet answered Find Ihe coofficiont of Iho X4 term in Ihe expansion of 10 Marked out 0( x2 2x Ix) Aie 20 Flag' question Select one: A 15 B. 120 C.240 D. 60 E.30 Next

3) 2"d term in expansion of (1+3y)

Find the 6th term of the binomial expansion: (xy)^10.

Consider the expansion of x(2x^2 + a/x)^7. The constant term is 20412. Find a.

Fifteen teams play in the Eastern Conference of the NBA. How many ways can the teams finish 1st, 2nd, 3rd, 4th, 5th, 6th, 7th, and 8th?

Assume that each of the n trials is independent and that p is the probability of success on a given trial. Use the binomial probability formula to find P(x): n = 19, X = 2, p =

Use the Binomial Theorem to find the coefficient of in the expansion of (x + 1)^10. The coefficient of

An employee consists of 17 men and 12 women. How many ways can this employee choose a committee of 3 men?

CURRENT OBJECTIVE: Find the number of combinations using the formula. Question: How many different exercise song combinations are possible if Cowaro can choose songs during his workout from a selection of 11 songs? Provide your desired number.

In how many ways can you answer a 15-question test if you answer each question with either "false" or "always false"? 100, 15 105, 25 None

There are 52 runners in a race How many ways can the runners finish first, second, and third? There are different ways that the runners can finish first through third (Type a whole number )

Evaluate 48C5 using technology or the formula

ANSWER FIVE QUESTIONS ONLY 94. UI SLJa & ISJIY 841 UIBIQO (e)l expansion of (2+x)

How can I calculate the average income? What is the average income of an individual?

The population standard deviation for the heights of dogs, in inches, in a city is 3.7 inches. If we want to be 95% confident that the sample mean is within 2 inches of the true population mean, what is the minimum sample size that can be taken?

The value zc is a value from the standard normal distribution such that P -zc x zc 5 c. 2. Statistical Literacy The point estimate

Find class boundaries, midpoint, and width for the class 123-143

A reading specialist in a large public school system believes that the more time students spend reading, the better they will do in school. She plans a middle school experiment in which an SRS of 30 eighth graders will be assigned four extra hours of reading per week, an SRS of 30 seventh…

The mean thrust of a certain model jet engine is 9500 pounds. Concerned that a production process change might have lowered the thrust, an inspector tests a sample of units, calculating a mean of 9350 pounds with a z-score of -2.46 and a P-value of 0.0069. Which of the following is the most…

All of the following statements are true for all discrete random variables except for which one? A. The possible outcomes must all be numerical. B. The possible outcomes must be mutually exclusive. C. The mean (expected value) always equals the sum of the products obtained by multiplying…

Given that the sample has a standard deviation of zero, which of the following is a true statement? A. The standard deviation of the population is also zero. B. The sample mean and sample median are equal. C. The sample may have outliers. D. The population has a symmetric…

Data are collected on income levels x versus number of bank accounts y. Summary calculations give = 32,000; sx = 11,500; = 1.7; sy = 0.4, and r = 0.42. What is the slope of the least squares regression line of number of bank accounts on income level?

It is estimated that 30% of all cars parked in a metered lot outside City Hall receive tickets for meter violations. In a random sample of 5 cars parked in this lot, what is the probability that at least one receives a parking ticket? A. 1 - (0.3)5 B. 1 - (0.7)5 C. 5(0.3)(0.7)4 D. 5(0.3)4…

A survey was conducted to determine the percentage of parents who would support raising the legal driving age to 18. The results were stated as 67% with a margin of error of ±3%. What is meant by ±3%? A. Three percent of the population were not surveyed. B. In the sample, the percentage of…

Leech therapy is used in traditional medicine for treating localized pain. In a double blind experiment on 50 patients with osteoarthritis of the knee, half are randomly selected to receive injections of leech saliva while the rest receive a placebo. Pain levels 7 days later among those…

Random samples of size n are drawn from a population. The mean of each sample is calculated, and the standard deviation of this set of sample means is found. Then the procedure is repeated, this time with samples of size 4n. How does the standard deviation of the second group compare with the…

We are interested in the proportion p of people who are unemployed in a large city. Eight percent of a simple random sample of 500 people are unemployed. What is the midpoint for a 95% confidence interval estimate of p? A. 0.012 B. 0.025 C. 0.475 D. p E. None of the above.

Suppose that 54% of the graduates from your high school go on to 4-year colleges, 20% go on to 2-year colleges, 19% find employment, and the remaining 7% search for a job. If a randomly selected student is not going on to a 2-year college, what is the probability she will be going on to a…

For their first exam, students in an AP Statistics class studied an average of 4 hours with a standard deviation of 1 hour. Almost everyone did poorly on the exam, and so for the second exam every student studied 10 hours. What is the correlation between the numbers of hours students studied…

The waiting times for a new roller coaster ride are normally distributed with a mean of 35 minutes and a standard deviation of 10 minutes. If there are 150,000 riders the first summer, which of the following is the shortest time interval associated with 100,000 riders? A. 0 to 31.7…

To test whether extensive exercise lowers the resting heart rate, a study is performed by randomly selecting half of a group of volunteers to exercise 1 hour each morning, while the rest are instructed to perform no exercise. Is this study an experiment or an observational study? A. An…

Suppose P(X) = 0.35 and P(Y) = 0.40. If P(X|Y) = 0.28, what is P(Y|X)?

A company has a choice of three investment schemes. Option I gives a sure $25,000 return on investment. Option II gives a 50% chance of returning $50,000 and a 50% chance of returning $10,000. Option III gives a 5% chance of returning $100,000 and a 95% chance of returning nothing. Which option…

Two commercial flights per day are made from a small county airport. The airport manager tabulates the number of on-time departures for a sample of 200 days. What is the χ2 statistic for a goodness-of-fit test that the distribution is binomial with probability equal to 0.8 that a flight…

From a group of 35 people, you have to choose 15 people for a sports team. How many different ways can you choose a group of this many people?

From a group of 35 people, you have to choose 21 people for a sports team. How many different ways can you choose a group of this many people?

From a group of 35 people, you have to choose 13 people for a sports team. How many different ways can you choose a group of this many people?

From a group of 35 people, you have to choose 12 people for a sports team. How many different ways can you choose a group of this many people?

From a group of 35 people, you have to choose 23 people for a sports team. How many different ways can you choose a group of this many people?

Find the inter quartile range of the following data set: 11, 23, 46, 65, 74, 98, 101

Find the inter quartile range of the following data set: 14, 54, 62, 65, 84, 91, 101

Find the inter quartile range of the following data set: 3, 4, 5, 19, 20, 21

Find the inter quartile range of the following data set: 103, 105, 107, 109, 111, 113

Find the inter quartile range of the following data set: 34, 64, 90, 165, 189, 200

A sample of 93 students has a mean weight of 41 kg. Find the Z score of a sample from a population with a mean weight of 79 kg and a standard deviation of 40 kg.

A sample of 78 students has a mean weight of 49 kg. Find the Z score of a sample from a population with a mean weight of 65 kg and a standard deviation of 92 kg.

A sample of 53 students has a mean weight of 30 kg. Find the Z score of a sample from a population with a mean weight of 92 kg and a standard deviation of 60 kg.

A sample of 59 students has a mean weight of 97 kg. Find the Z score of a sample from a population with a mean weight of 36 kg and a standard deviation of 65 kg.

A sample of 85 students has a mean weight of 85 kg. Find the Z score of a sample from a population with a mean weight of 33 kg and a standard deviation of 93 kg.

Explain what the mean is, the formula and calculate it for the following set of numbers: 72, 18, 77, 75, 82

Explain what the mean is, the formula and calculate it for the following set of numbers: 46, 13, 61, 89, 87

Explain what the mean is, the formula and calculate it for the following set of numbers: 43, 1, 87, 34, 24

Explain what the mean is, the formula and calculate it for the following set of numbers: 70, 45, 3, 99, 33

Explain what the mean is, the formula and calculate it for the following set of numbers: 96, 9, 56, 37, 46

82 students enter a contest at school. The contest offers a first, second, and third prize. How many different combinations of 1st, 2nd, and 3rd place winners can there be?

71 students enter a contest at school. The contest offers a first, second, and third prize. How many different combinations of 1st, 2nd, and 3rd place winners can there be?

52 students enter a contest at school. The contest offers a first, second, and third prize. How many different combinations of 1st, 2nd, and 3rd place winners can there be?

79 students enter a contest at school. The contest offers a first, second, and third prize. How many different combinations of 1st, 2nd, and 3rd place winners can there be?

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