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Intro Stats / AP Statistics Q&A Archive of August 8, 2022

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August 8 of 2022

j) You wish t0 create a 5 digit number from all digits; 0 12 3 4 5 6 7 8 9 Repetition is not allowed 0 cannot be first as it does nct count as & place value if it is first. le. 027 is a 2 digit numb How many even numbers can YOU have?
Six students will be arranged in @ row of chairs for picture taking and two of these students must be placed on either both ends of the row: Which of the following statements can be done to identify the number of arrangements of the six students? Group the two particular students and get the…
Title to Detect Factorials 6! + 4 (√2) * (√3)
What Have I Learned? Ms. Casabuena is planning to buy a new car. There are 2 available body styles: sedan or hatchback and 5 colors: blue, black, gray, red, and pink. How many different choices of body styles and colors can she choose? Body Styles: Sedan (S) Hatchback (H) Colors: Blue…
If P(n) = 336, which of the following are possible values of n and r? n-6, r=4 n-8, r=3 n-7, r=3 n-9, r=2 What is the permutation notation of 10 students sitting in 10 front seats of an auditorium? A P(10,10) B P(10,9) C P(10,9) D P(10,9)
5. Find the number of permutations of 11 objects taken 10 at a time.
5. How many 2-digit numbers can be formed from the numbers 1, 2, 3, 4, 5, and 6 if the digits are to be repeated.
Columnale. Now, how many outfits can you put together? In how many ways can 6 bicycles be parked in a row? 5. How many 2-digit numbers?
27.) A math debating team consists of speakers. How many ways can the captain and vice captain be chosen? A. 1 round table: In how many ways can they sit? 28.) At a dinner party, men and 6 women sit. Bryan and Jell must sit together. C. J12 < 21 A. 21*10 D. 2! + 12! B. 124 101…
C1" €als ),Uz slow" 5 Wo &06g j 1 ~l i 4 How many 4-digit even numbers can be formed from the digits 5, 6, 7, 8, 9 if no digits are repeated?
A committee of 8 will be selected from a group of 14 students from Grade 10. How many different committees can be formed?
If a combination lock must contain 3 different digits without repetition, in how many ways can a code be formed from the digits 0 to 9?
B 4 During the Mathematics class, Mr. Laluz asks his students how many 2-digit numbers can be made from the numbers 1, 2, 3, and 4, when repetition is not allowed? A. 8 B. 12 C. 16 D. 24 Tac Pe Jcea: salad where she can choose one from each of the following ingredients:
The six digits of the number 738925 are rearranged so that the resulting six-digit number is even. Find the number of different ways in which this can be done. [2]
Activity 2: Evaluate each (Show your solution) 1. 8C 2. 8C2 6Cz 3. sCo
Lesson 1: Permutation of n taken r at a time: In how many ways can 7 men sit in a row of 5 chairs?
Which term refers to the arrangement of a set of objects wherein the order is not important? A Permutation B. Combination C Order D. probability 2_ What is the value of 12C4? A 560 B. 495 C.240 D. 120
How many ways are there for 15 runners to finish in 1st, 2nd, and 3rd place? (2 pt) In a 4/35 lottery, you choose 4 numbers from 1 to 35. If your numbers match the state's numbers, you win the jackpot. How many ways are there to select 4 numbers if order does not matter?
23. In how many different ways can the letters of TITTIVATING be arranged? a. 77 b. 277200 c. 34650 d. 48650 e. 69300 24. A committee of 5 people is to be chosen from a group of 12 people
How many permutations are possible of letters in the word "HOUSE"?
Text: Directions: Solve each problem below; Write your answers on a separate sheet of paper. Two raffle tickets will be drawn from 30 raffle tickets; thus, 2 and n. A catering service offers 8 appetizers, 10 main dishes, and desserts. In how many ways can the feast committee…
How many 4 letter combinations will be formed from the letters of the word HONESTLY? Interpretation; Solution:
There are 12 finalists in a dance competition. How many ways can gold, silver and bronze medals be awarded tO them? 2. In your class, there are 15 qualified candidates to be elected as classroom officers_ If vou are going to OM
(iv) 25 24 C22 C21
rample 2. Evaluate 3! + 7! 31 + 71=(3 ,201) + (7.6+5.4.3.2. =6 + 5,040 =5, 046
7. If P(5,3) = n, then n = _____ A. 10 B. 15 C. 60
11 + 3 = 14. 31 ÷ 81 = 0.38. 51 - 31 + 4 = 24. √16 = 4.
in sitting beside each other? 2. In how many ways can YOU arrange 5 Mathematics books Science books, and 3 English books on & shelf such that books of the same subject are kept together? 3. In how many ways can 5 children be arranged in a line such that
17. In how many ways can letters of the set {R, S, T, U} be arranged to form ordered codes of 2 letters? (no letters are repeated) A. 16 B. 72 C. 12 D. 120
Identify whether the given situation is a permutation or combination by writing its correct set-up (nPr / nCr) and answer.
Given X, Y, Z, list all the possible ways you can arrange them 2 at a time in a row. Given +, -X, +, list all the possible ways you can arrange them 3 at a time in a row.
15. What is rif C(6,' r) =20? a. 1 b. 2 c.3 d
How many numbers of three different digits can be formed from the integers 1, 2, 3, 4, 5, 6? Determine the number of possible five-digit telephone numbers if none of the first two digits can equal zero and any digit can be used for the remaining numbers.
If repetition of digits is allowed, how many 4-digit numbers can be formed from 0, 1, 2, and 3? a. 500 b. 450 c. 600 d. 550
In how many ways can 20 distinct frogs be arranged in a row for an experiment when only three frogs can be displayed at a time? A. 4570 B. 7,520 C. 840 D. 5,110 Evaluate √(6^2) A. 120 B. 50 C. 30 D. 15 How many distinct permutations can Maria make from the word MISSISSIPPI? A. 41,214
5 must be thc frst digit, 2 is the second digit, and repetition of digits is allowed? A) 6 B) 8 Ci 4 14.5 must be the first digit, 2 is the last digit, and repetition of digits is not allowed? A) 16 B} 8 D) 2 How many permutations there in the letters of the word HELPING if ING must stay…
A restaurant offers four sizes of pizza, two types of crust, and eight toppings. How many possible combinations of pizza with one topping are there?
Tou Tave 0 peupie Youi ciud Mo Many Woys cdnyou chouse Ftesidem; Secretary? There are 5 colors to choose from, how many unique 3 color flags can be made? You need to pick three people to be in a committee There are 7 people t0 pick frc different committees Gn voumake?
Caterer offers 2 kinds of soup, 2 kinds of meat dish, 1 vegetable dish, and 2 kinds of fish dish. Out of these dishes, the caterer wants to have 100 distinct menu options. How many possible combinations of soup, meat dishes, fish dishes, vegetable dish, and desserts are there? Support your…
Julia cannot remember a 7-character password she created years ago, so she decides to just try all the possibilities until she finds it. The first 2 characters of the password are numerical digits (0-9), and the last 5 characters are letters. both digits and letters can repeat; how many…
A family of 8 can be seated around a circular table with 8 chairs. 7. In how many ways can 368,720 members be seated in a round table? 4,032, 5,040 If a certain four people are seated side by side? 576, 144, 396
Which of the following derives the formula of permutations of objects taken r at a time? P(n,r) = n! / (n-r)! C.P(n) = n! / (n-r)! P(n,r) = n! / (n-r)! P(n,r) = n! / (n-r)! Which solution is the same as P(9,5)? 9 x 5 9 x 8 x 7 x 6 x 5 9 x 8 x 7 x 6 x 5 x 4 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 When…
Different samples of size n-3 can be selected from a population with the following sizes: A. N=5 B. N=15 C. N-7 D. N-13
How many different 4-digit numbers can be formed from the digits 1, 3, 5, 7, and 9 if repetition of digits is allowed? 225, 100, 125, or 625?
In how many ways can 5 learners stand in a circular to play a game? A teacher wants to assign different tasks to her learners. In how many possible ways can she do it? How many distinct permutations of the letters of the word PHILIPPINES are there? Nnm W choose cleaners from 20 learners?
Q3. In the expansion of (2 find the 7th term:
15. Calculate C(20, 7) A. 77 520 B. 77 250 C. 77 025 D. 77 052 Checked and Reviewed by:
On the plane; there are 6 diflerent points (no 3 of them are lying on the sare line) . How many segments can be drawn by joining all the points? Thc School Chess Club has members_ In how may many ways ca 3 members of the club be chosen for the Rules committee?
a. 720 b. 700 c. 36 d. 30 3. In how many ways can 8 people be seated around a circular table if two of them insist in sitting beside each other?
The bowl contains red marbles, yellow marbles, and blue marbles. In how many ways can the balls be selected given each condition? If all the marbles are yellow, how many are there exactly?
Given: n = 5 Solution: Plan;) 0 = 1 P(5,3) = 0.1412.60 (5 - W)
Evolving Permutations and Combinations: In this module, you are expected to solve problems involving permutations and solve problems involving combinations. How many organizations are there? 20.3 How many? 10. How? What I Know: Directions: Encircle the letter of the correct answer: What…
15. There are 4 different Mathematics books, 3 different Arts books, and 5 different History books. In how many ways can the books be arranged on a shelf if the History books are kept together? A. P(12,5) B. P(8,5) C. P(8,5) D. P(5,5) E. P(8,8) P(5,5)
17.. In how many ways can a committee of three be formed from a group of 10 members? A. 480 B. 360 C. 240 D. 120
Spaces available, in how many different ways can this be done? There are only 3. In how many ways can 10 different books be arranged on a shelf?
Text: Determine if the given situation is a Permutation or Combination 10 points Permutation Combination For a survey, students are chosen from a group of 10 students. Pull out 3 coins from my purse that consist of a five-centavo coin, a ten-centavo coin, a peso coin, a five-peso coin, and a…
A closet has 4 shirts, 3 pants, 2 hats and 4 pairs of shoes. How many possible outfits can be made, using one of each kind?
Permutations? 5. Which of the following conditions involves your Facebook account? The arrangement of letters in the password often confuses three students from your class. The order of the winners in the contest is [I II & HI I & HII L,4 & I].
Directions: Write the following problem in Permutation notation: Eric wanted to arrange his collection of books on the bookshelf. He has 10 books. In how many ways can he arrange them if there are only 7 available spaces?
CIRCULAR or BLITHER of these Write your Tell each arrangement is LINEAR; number answer on the space before each 1. Digits in an eight-digit number Plates on the table 3. Horses on carousel
How many different permutations of letters can be made in the word BASKETBALL? 907,200 3,628,800 362,880
In how many ways can girls and boys be arranged in a row so that all three girls are together? If repetition is not allowed, how many three-digit numbers can be formed from the digits 3, 4, 5, 7, 8, and 9? How many of them are even? How many of them are greater than 400? How many of them are…
Great! You have reached this part of the module. Ensure your full understanding of the concepts of permutations and combinations. It is important that you are able to complete each statement below. Fill the blanks with correct words. Permutation is used when order is taken into consideration,…
II. Solve as indicated SHOW SOLUTIONS Find the number of permutations of the letters of each word. (2 points each) MALAKAWAYAN BANABA 2. ANONANG BAKAWAN 3.0 ANTIPOLO
D. If there are 3 men and 3 women in a round table; in how many ways can they be seated if two particular woman must not sit together? Distinguishable and circular permutation
A list of possible judges is composed of seven women and five men. How many different juries can be formed from the list if: the jury consists of four women and three men? the jury consists of two women and four men? the jury consists of five judges with at least one man?
Ashrtey has seven CDs on his desk. In how many ways can he select three CDs? 0.45 I5 Four out of seven students are needed to hand out programs at the drama club performance. In how many ways can the four students be chosen?
How many ways can we arrange the letters A, B, and C?
1) n= 4 Cz 3 4 P & : 4! C4-5).
How many distinguishable ways can you arrange the letters in the word ACCOUNTANCY such that all vowels are together?
The word "ARTICLE" has nine letters. How many permutations and last positions of consonants in the word?
Test V; Find the combination. Choose your answer in the box below and write the letter of your answer in the space provided: 19448 b; 495 C165 d231 e: 300 C(11,8) (25,23) 3. C(17,10) 4. C(22,20) 5. C(12,8)
4 different objects can be arranged in ways
Name: Activity 4 Part 2: Solving Problems Involving Permutations In a group study, women and 3 men sit in a circle. How many ways can this be done if there are no restrictions? 1) Men and women alternate. 2) Alex and Ramela sit together. 3) Alex, Ramela, and Sam sit together. 4) Arlene,…
1) P(11, 4) Answer: P = 7920
Find the value of the indicated term in P. nPc "hint for the answer 206 The average number of adult human bones 232 The number of letters of the longest English word without consonant 352 The atomic number of Calcium in the Periodic Table 4560 The number of island groups in the Philippines 526…
How many line segments can be formed from 6 given points with no three of which are collinear? Given: n = 6, T = 2 Formula: n! / (n - r)! * r! = 6! / (6 - 2)! * 2! = 6! / 4! * 2!
Ikxk < 1,- is of (l + kr) + 2. Given that the binomial expansion 1 - 6r + Ax + ... (a) Find the value of the constant k. Simplest form: Find the value of the constant A, giving your answer in its...
If there are 10 points on a plane, 4 of them are collinear and no other 3 points are collinear, how many lines are formed?
When a pair of dice is rolled, in how many ways can the sum of the two numbers be 7?
Learning Task J: Derive and Find the formula for finding the number of combinations in the following situations: Looking at the beautiful sky of a very peaceful night, Constellation Libra; it has shown six stars, you recognize the distinct points on a plane. How many polygons can be formed? In…
Evaluate 6! + 2! a. 722 b. 622
7.A soloist is auditioning for a point musical play: If she is required to sing any three of the 7 prepared songs, in how many ways can she make her choice? A. 325 B. 320 C.315 D. 310
1. Find the number of distinguishable permutations of the letters in the word PHILIPPINES. 2. Find the number of ways can 6 people be seated in a circular table.
Which of the following is true in the definition of factorial? nl = (n-1) (n-2) (n-3) nl = n(n-1) (n-2) (n-3) nl = (n-1) (n-2) (n-3) 3(2)(1) nl = n(n-1) (n-2) 3(2)(1)(0)
Text: Fn Matching Type: Choose the letter at Column B for the appropriate formula that will give the permutation of the given problem at Column A. Write your answer on a separate sheet of paper: 0/4 Is P = plHl qi 19 I5 i+ ju jOT P = pl rl 9l 19 It '01 S1 How are you today? Did you sleep well…
Dineclons Solve each problem. Show your solution following the Fundamental Counting Principle. Write your answer in the second column. Word Problems: How many 2-digit numbers can be formed from 9 numbered digits if repetition of the digit is not allowed? Answer: How many 4-digit numbers can…
SAQ-1: How do you solve permutation questions/problems? SAQ-2: Is there a need to consider the formula in finding the number of permutations of objects? Why? Let's Practice! (Use separate sheets for your answers.) Activity: Evaluate the following: 54, 91, 104 P(6,6), P(8,3) B. Solve each…
Read each combination value directly from Pascal's Triangle: 5C4 OA = 4 OB = 5 OC = 120 OD = 20
How many ways can a committee of at least 4 people be formed from a group of 6 people?
4!6!/2!5! Simplify your answer as much as possible.
1. How many different ways can 18 questions on a true-false test be answered if a student answers every question? 262484 262254 261654 262144
Algebraically determine the coefficient of m^4n in the expansion of (3m + 2n)^7.
James is choosing a four-digit Passcode for his smartphone. How many different Passcodes are possible? There are ten digits that James can choose from.
How many ways can the letters in the word RIFFRAFF be arranged?
A group of 28 people need to take an elevator to the top floor. The elevator can fit seven. How many ways can they choose a group of 7 to ride the elevator on the first time? 1,213,060 7,104,240 592,020 1,184,040
2. One of the terms in the binomial expansion of (3 + ar);; where a is & constant; is 540+' Find the possible values of a.
A Track and Field relay team consists of 4 team members lined up in order around a track in the 4 x 100 meter relay. How many different line-ups are possible if the 4-man relay team is chosen from among 6 possible team members?
Tina must select and answer in any order two of nine essay questions on a test. In how many ways can she do so?
If all the letters of the word ARRANGE are arranged in all possible ways, in how many of - Words We Will have thc A's not together and also the R's nol together:
1. A group of five students is to be chosen from a 45-member class to represent the class on the student council. How many ways can this be done?
In a room of 5 people, how many different handshakes are possible?
ActivityZ Matching Type: Match Column B with Column A Write the letter of the correct answer: Column B Column A 1. 6Pa A. 40,320 2. BPv B. 24,024 3. :Pa* sP4 C. 720 4. 9P, = 72 D. 120 5. 4! E. 24
Seven red, three green, and five yellow marbles are to be arranged. All the marbles of the same color are not distinguishable from each other. How many different arrangements are possible?
For items no: 1-5, Janna celebrates her 18th birthday. She invited six of her closest friends (3 boys and 3 girls). Find the number of arrangements with the following restrictions: - They are all seated at a round table. - Boys and girls are seated alternately. - All boys sit together. - Four…
3. In how many ways can Myrna arrange 8 potted plants in a row?
Exercise 2. Directions: Solve the following problems on your answer sheet 2. How many ways can you arrange 5 distinct objects taken 3 at a time if repetition is allowed?
LEARNING TASK 3: How many permutations can be made from the letters in the following words: PHILIPPINES, MISSISSIPPI, GULANG, GULANG, ' .(, MATATALINO, IBABANG, IYAM
How many ways can the letters of the word PHOENIX be arranged?
A die and a coin are tossed. How many outcomes are possible?
5. How many four-digit numbers can be formed from the numbers 1, 3, 4, 5, 6, 8, and 9 if repetition of digits is not allowed? A. 720 B. 540 C. 360 D. 840
P(8, r) = 6 720
Error plate number consists of a four-digit number followed by three English alphabet. How many motorcycle plates are possible?
arrange his guests around a dining table? Find the number of different ways that a family of 7 can be seated around a circular table with 7 chairs.
How many two-letter subsets can be made from the set of letters {A, K, O} if order is important?
Evaluate the following: C (4_ C(,3)+C (11,9) C (9,4)-C (9,5) C (13,r) =286 C (n,2)= 56
3. Evaluate: 8P3 336 6720 24 56
Use the Binomial Theorem to prove that (E - o(k))^2k = 3^k
What is 6P4 =? b. 24 d. 360
15 How many eleven- letter patterns can be formed from the letters of the word Mississippi ? A. 11! B. 11! / (4!4!2!) C. (11-1)! D. 11! / (4!3!2!)
2. How many ways are there to seat 6 people around a round table for lunch? 100 120 700 5040
Ben & Jerry's ice cream has 9 different flavors, offer 3 different sizes and you can choose a sugar cone, or a cup. How many outcomes are in the sample space? Just type a number:
Eight students are seated at a round table In how many ways can they be seated if three of them insist on sitting next to each other?
10. How many 4-digit odd numbers can be formed from the digits 1, 2, 3, 4, & 5 if repetition is allowed?
14. How many different quadrilaterals can be formed from 8 non-collinear points on a plane? A. C(8,5) B. P(8,5) C. C(8,4) D. P(8,4)
In a group of 10 people, five Php15,000 prizes will be given. How many ways can the prizes be distributed?
19. Find the number of distinguishable permutations of the letters SWEET. A. 30 B. 60 C. 90
TEST I. Evaluate and simplify the following given. (Write only the answer. Example: 50) 1) 4!
ACTIVITY 2: Permutation and Combination Tell whether a given problem situation involves Permutation or Combination then solve: 13. A bank plans to assign an identification number to each account: Each account number will have five digits, and no digit will be repeated: How many different…
8, If C (n, 4) = 35, what is n? A. 5 B. 6 D. 8
6. From 20 qualified applicants, in how many ways can 8 teacher applicants be chosen?
How many ways can identical pen sets and identical watches be given to the graduates each receives one item?
How many permutations are there in the word BALLOON?
1. Ten points are randomly placed on a circle_ In how many different ways can you form each geometric figure? Show your solution) A Triangle (2 pts) D. Heptagon (2 pts) B Quadrilateral (2 pts) E. Octagon 2 pts) C. Pentagon (2 pts) 2. How many polygons can be formed from & non collinear points…
DJ Cynthia is making a playlist for a radio show. She is trying to decide what 10 songs to play and in what order they should be played.
Use the binomial theorem to answer this question for: (4xy)^2. Show the summation notation equation to express this expansion. x^(-k)y^k * kC(n - k) (c) Using the equation you wrote in part (a), use it to determine the third term of this expansion (show work). Have the coefficient in your…
Name: Directions: Determine the values of n and/or r: (2 pts each) (Written Work) 1. P(n, 2) = 30 2. P(7, r) = 840 3. C(n, 10) = 3C(n, 9) 4. C(13, r) = 286 5. C(n, r) = 4 and P(n, r) = 24
There are 13 female board members and 17 male board members. How many ways are there to make a committee of 16 board members? How many ways are there to make a committee of 16 board members if exactly 6 must be female?
There are 7 runners in & race. How many different ways can the 7 runners finish the race, assuming there are no ties? 49 B 5,040 28
Find the circular permutations of 15 students seated around a circular table. Your 13 friends are sitting at a round table. Find the number of ways they can be arranged. Your mother made 5 side dishes. How many ways can she arrange them at a round table? Find the number of ways that a family of…
3. In how many ways can 5 men and 5 women be seated at a round table if there is no restrictions?
14 In how many ways can two blue marbles and four red marbles be arranged in a row? a 5 b 15 c 20 d 30
For numbers 6-11. Read the situation and answer the following questions: A box of Mrs. Donut contains 6 honey dipped, 6 Bavarians, and 7 chocolate-filled donuts. 6-7. How many ways can 5 Bavarian donuts be selected? a. 5 C d. 8 b. 8 8-9. How many ways can 2 chocolate-filled donuts be…
In a wedding reception, five couples, including the groom and bride, want to have their picture taken: In how many ways can they arrange themselves in a row if couples must stay together?
12. If P(n, r) = 120, which of the following are possible values of n and r? A. n = 6, r = 4 B. n = 7, r = 3 C. n = 6, r = 2 13. In how many ways can Jenny choose three flavors from six flavors of milk tea? A. 20 B. 12 C. 10 D. n = 7, r = 4 D. 120
5) How many 5-digit odd numbers can be formed from the digits 1, 2, 3,4, and without repetition?
Find the number of ways in which 5 people A, B, C, D, and E can be seated at a round table, such that A and B must always sit together, but C and D must not sit together.
Answer the following problems by applying the concepts of permutations. How many emails can be formed from using two English alphabets and four digits if there is no restrictions?
In an All-Area track meet, 271 sprinters enter a 200-meter dash competition. The track has 7 lanes, so only 7 sprinters can compete at a time. At the end of each race, the six non-winners are eliminated, and the winner will compete again in a later race. How many races are needed to determine…
In how many ways can 8 different books be arranged on a shelf? 40,320 8 5760 5040
Evaluate the following: 1.51 2. 3141 3.6121 L (2-4 16-1 (20- 18)' 9. P(6, 31 10. P(3 , 31 7980 120 130 144 #1 #2 #3 #4 #5 #6 #7 #8 #9 #10
From a standard 52-card deck, how many 7-card hands contain all clubs? A hand of 7 clubs can be chosen in ? ways.
How many different 7-digit numbers can be formed from the digits 0, 1, 2, 2, 3, 3 assuming that no number can start with 0? b) How many of these numbers will end in 0?
ACTIVITY 2: Answer the given item completely. Show your solution. (5 points): PERFORMANCE TASK In how many ways can the letters of the word MATHEMATICS be arranged ina row?
C. Solve for the unknown value of n by filling the blank(s): nPz = 12 n! / (n-2)! = 12 n(n-2) = 12 n^2 - 2n = 12 n^2 - 2n - 12 = 0 (n-4)(n+3) = 0 n = 4 n = -3
MULTIPLICATION COUNTING RULE 4. Your school offers two English classes, three math classes and three history classes. You want to take one of each class. How many different ways are there to organize your schedule? Solution:
Answer the following questions correctly and you will get a summoning scroll and 10K coins. 1/10 Lucy wants to wear different clothes every day. She has dresses, pairs of shoes, and pairs of earrings. Lucy could choose a dress, a pair of shoes, and a pair of earrings every day. However, some…
Sample space, probability, permutation, d. sample space. 5. In how many ways can you arrange 8 books on a shelf if only 5 books can fit at a time? 6,920 ways. b. 6,820 ways. 6,720 ways. 6,420 ways. 6. It is a numerical value that describes the likelihood that an event will happen or not.
Screenshot the problem and scan it with the Gauthmath app; enter the answer, and earn 200 Coins. In an All-Area track meet, 271 sprinters enter a 200-meter dash competition. The track has 7 lanes, so only sprinters can compete at a time. At the end of each race, the six non-winners are…
4. Using the letters of the word INTERMITTENT how many 12-letter arrangements can be formed: without restrictions (2 marks) if each word begins with T and ends with N (2 marks) if the 4 T's are together (2 marks) if each word begins with 2 T's (2 marks) if each word begins with exactly 2 T's (2…
The coefficients in the expansion of (x+y) can be found using a row of Pascal's triangle.
OE "0 How many three-digit numbers composed of different numbers can be formed from 0, 2,3, 5, and 67
There are 26 boys and 28 girls in a rugby club. Sophia selects two girls from the club. How many ways of choosing are there?
3 1 1 3 0 64, { # $ # ; 2 : L 6 1 C
Determine the 20"h term in the expansion of '-y)
Nov 1st, Students from the 17-member assembly committee of 14 principals would like to know how many different committees can be chosen for the student council.
Use the Binomial Theorem to expand the expression (x+y5) (Simplify your answer )
If automobile license plates consist of four letters followed by one digit bow many different possible license plates are possible if letters ad numbers may be repeated? Select One 676,000 45.697.600 456.976.000 1.757.600 None of These
What is the value of the 6th term of the expansion (a + b)^9? 0 84a * 66 0 844663 126a^4 05 1260564
A In R, what does n stand for?
Question 10 (2 points) Algebraically determine the coefficient of mn in the expansion of (3m + 2n)
are greater than 50 million can be created many even eight digit numbers that 7 How 0,2,2,3,4,5,9, 9 ? using all the digits
12 In how many ways could 15 different books be divided equally among 3 people?
Expand (x + 5) 4 using Pascal's triangle (x+5)4 (Simplify your answer )
40 people are randomly selected and the accuracy of their wristwatches is checked, with positive errors representing watches that are ahead of the correct time and negative errors representing watches that are behind the correct time. The 40 values have a mean of 99 sec and a standard deviation…
Find the standard deviation of the following data set. Assume the data set is a sample. Round your answer to the nearest hundredth, if necessary. 35,70,31,37,65,38,38,44,43,43,68
A researcher randomly purchases several different kits of a popular building toy. The following table shows the number of pieces in each kit in the sample. Find the median of the data. Building Toy Pieces 160 45 265 350 350 45 104 296 265 109 170 208
Grocery Retailers Association of South Africa (GRASA) believes that the average amount spent on groceries by Cape Town shoppers on each visit to a supermarket is R175. To test this belief, the association commissioned Market Research e-Afrika to conduct a survey among a random sample of 360…
2.1 Bertino et al. (A-3) conducted a study to examine prospectively collecied data on gentamicin in pharmacokinetics in three populations over 18 years of age: patients with acute leukemia, patients with other nonleukemic malignancies, and patients with no underlying malignancy or…
find the critical valve zc that corresponds to a 90% confidence level.
Suppose the correlation between two variables is r = 0.19. What is the new correlation if 0.23 is added to all values of the x-variable, every value of the y-variable is doubled, and the two variables are interchanged?
A plant manager wishes to determine the difference in number of accidents per day between two departments. She wants to be 90% certain of the difference in daily averages to within 0.25 accidents per day. Assume standard deviations of 0.8 and 0.5 accidents per day in the two departments,…
Taxicabs in a metropolitan area are driven an average of 75,000 miles per year with a standard deviation of 12,000 miles. What is the probability that a randomly selected cab has been driven less than 100,000 miles if it is known that it has been driven over 80,000 miles? Assume a normal…
Suppose the probability that a person picked at random has lung cancer is 0.035 and the probability that the person both has lung cancer and is a heavy smoker is 0.014. Given that someone picked at random has lung cancer, what is the probability that the person is a heavy smoker?
Which of the following is not true about t-distributions? A. There are different t-distributions for different values of df (degrees of freedom). B. t-distributions are bell-shaped and symmetric. C. t-distributions always have mean 0 and standard deviation 1. D. t-distributions are more…
To conduct a survey of which long distance carriers are used in a particular locality, a researcher opens a telephone book to a random page, closes his eyes, puts his finger down on the page, and then calls the next 75 names. Which of the following is a correct statement? A. The procedure…
Following is a histogram of ages of people applying for a particular high school teaching position. Which of the following is a correct statement? A. The median age is between 24 and 25. B. The mean age is between 22 and 23. C. The mean age is greater than the median age. D. More…
A local school has seven math teachers and seven English teachers. When comparing their mean salaries, which of the following is most appropriate? A. A two-sample z-test of population means B. A two-sample t-test of population means C. A one-sample z-test on a set of differences D. A…
Which of the following is a false statement about simple random samples? A. A sample must be reasonably large to be properly considered a simple random sample. B. Inspection of a sample will give no indication of whether or not it is a simple random sample. C. Attributes of a simple random…
Suppose that the regression line for a set of data, y= 7x + b, passes through the point (-2, 4). If and are the sample means of the x- and y-values, respectively, then y=
To study the effect of alcohol on reaction time, subjects were randomly selected and given three beers to consume. Their reaction time to a simple stimulus was measured before and after drinking the alcohol. Which of the following is a correct statement? A. This study was an observational…
What is a placebo? A. A method of selection B. An experimental treatment C. A control treatment D. A parameter E. A statistic
The graph below shows cumulative proportions plotted against numbers of employees working in mid-sized retail establishments. What is the approximate interquartile range? A. 18 B. 35 C. 57 D. 68 E. 75
The empirical rule is commonly used in which branch of statistics? Descriptive statistics Inferential statistics All of the above Page 1 of 15 Next Page
The label on a package of cords claims that the breaking strength of a cord is 3.5 pounds, but a hardware store owner believes the real value is less. She plans to test 36 such cords; if their mean breaking strength is less than 3.25 pounds, she will reject the claim on the label. If the…
Suppose that 60% of a particular electronic part last over 3 years, while 70% last less than 6 years. Assuming a normal distribution, what are the mean and standard deviation with regard to length of life of these parts? A. μ = 3.677, σ = 3.561 B. μ = 3.977, σ = 3.861 C. μ = 4.177, σ =…
Consider a hypothesis test with H0 : μ = 70 and Ha : μ < 70. Which of the following choices of significance level and sample size results in the greatest power of the test when μ = 65? A. α = 0.05, n = 15 B. α = 0.01, n = 15 C. α = 0.05, n = 30 D. α = 0.01, n = 30 E. There is no way of…
In comparing the life expectancies of two models of refrigerators, the average years before complete breakdown of 10 model A refrigerators is compared with that of 15 model B refrigerators. The 90% confidence interval estimate of the difference is (6, 12). Which of the following is the most…
The parallel boxplots below show monthly rainfall summaries for Liberia, West Africa. Which of the following months has the least variability as measured by interquartile range? A. January B. February C. March D. May E. December
j) You wish t0 create a 5 digit number from all digits; 0 12 3 4 5 6 7 8 9 Repetition is not allowed 0 cannot be first as it does nct count as & place value if it is first. le. 027 is a 2 digit numb How many even numbers can YOU have?
Six students will be arranged in @ row of chairs for picture taking and two of these students must be placed on either both ends of the row: Which of the following statements can be done to identify the number of arrangements of the six students? Group the two particular students and get the…
Title to Detect Factorials 6! + 4 (√2) * (√3)
What Have I Learned? Ms. Casabuena is planning to buy a new car. There are 2 available body styles: sedan or hatchback and 5 colors: blue, black, gray, red, and pink. How many different choices of body styles and colors can she choose? Body Styles: Sedan (S) Hatchback (H) Colors: Blue…
If P(n) = 336, which of the following are possible values of n and r? n-6, r=4 n-8, r=3 n-7, r=3 n-9, r=2 What is the permutation notation of 10 students sitting in 10 front seats of an auditorium? A P(10,10) B P(10,9) C P(10,9) D P(10,9)
5. Find the number of permutations of 11 objects taken 10 at a time.
5. How many 2-digit numbers can be formed from the numbers 1, 2, 3, 4, 5, and 6 if the digits are to be repeated.
Columnale. Now, how many outfits can you put together? In how many ways can 6 bicycles be parked in a row? 5. How many 2-digit numbers?
27.) A math debating team consists of speakers. How many ways can the captain and vice captain be chosen? A. 1 round table: In how many ways can they sit? 28.) At a dinner party, men and 6 women sit. Bryan and Jell must sit together. C. J12 < 21 A. 21*10 D. 2! + 12! B. 124 101…
C1" €als ),Uz slow" 5 Wo &06g j 1 ~l i 4 How many 4-digit even numbers can be formed from the digits 5, 6, 7, 8, 9 if no digits are repeated?
A committee of 8 will be selected from a group of 14 students from Grade 10. How many different committees can be formed?
If a combination lock must contain 3 different digits without repetition, in how many ways can a code be formed from the digits 0 to 9?
B 4 During the Mathematics class, Mr. Laluz asks his students how many 2-digit numbers can be made from the numbers 1, 2, 3, and 4, when repetition is not allowed? A. 8 B. 12 C. 16 D. 24 Tac Pe Jcea: salad where she can choose one from each of the following ingredients:
The six digits of the number 738925 are rearranged so that the resulting six-digit number is even. Find the number of different ways in which this can be done. [2]
Activity 2: Evaluate each (Show your solution) 1. 8C 2. 8C2 6Cz 3. sCo
Lesson 1: Permutation of n taken r at a time: In how many ways can 7 men sit in a row of 5 chairs?
Which term refers to the arrangement of a set of objects wherein the order is not important? A Permutation B. Combination C Order D. probability 2_ What is the value of 12C4? A 560 B. 495 C.240 D. 120
How many ways are there for 15 runners to finish in 1st, 2nd, and 3rd place? (2 pt) In a 4/35 lottery, you choose 4 numbers from 1 to 35. If your numbers match the state's numbers, you win the jackpot. How many ways are there to select 4 numbers if order does not matter?
23. In how many different ways can the letters of TITTIVATING be arranged? a. 77 b. 277200 c. 34650 d. 48650 e. 69300 24. A committee of 5 people is to be chosen from a group of 12 people
How many permutations are possible of letters in the word "HOUSE"?
Text: Directions: Solve each problem below; Write your answers on a separate sheet of paper. Two raffle tickets will be drawn from 30 raffle tickets; thus, 2 and n. A catering service offers 8 appetizers, 10 main dishes, and desserts. In how many ways can the feast committee…
How many 4 letter combinations will be formed from the letters of the word HONESTLY? Interpretation; Solution:
There are 12 finalists in a dance competition. How many ways can gold, silver and bronze medals be awarded tO them? 2. In your class, there are 15 qualified candidates to be elected as classroom officers_ If vou are going to OM
(iv) 25 24 C22 C21
rample 2. Evaluate 3! + 7! 31 + 71=(3 ,201) + (7.6+5.4.3.2. =6 + 5,040 =5, 046
7. If P(5,3) = n, then n = _____ A. 10 B. 15 C. 60
11 + 3 = 14. 31 ÷ 81 = 0.38. 51 - 31 + 4 = 24. √16 = 4.
in sitting beside each other? 2. In how many ways can YOU arrange 5 Mathematics books Science books, and 3 English books on & shelf such that books of the same subject are kept together? 3. In how many ways can 5 children be arranged in a line such that
17. In how many ways can letters of the set {R, S, T, U} be arranged to form ordered codes of 2 letters? (no letters are repeated) A. 16 B. 72 C. 12 D. 120
Identify whether the given situation is a permutation or combination by writing its correct set-up (nPr / nCr) and answer.
Given X, Y, Z, list all the possible ways you can arrange them 2 at a time in a row. Given +, -X, +, list all the possible ways you can arrange them 3 at a time in a row.
15. What is rif C(6,' r) =20? a. 1 b. 2 c.3 d
How many numbers of three different digits can be formed from the integers 1, 2, 3, 4, 5, 6? Determine the number of possible five-digit telephone numbers if none of the first two digits can equal zero and any digit can be used for the remaining numbers.
If repetition of digits is allowed, how many 4-digit numbers can be formed from 0, 1, 2, and 3? a. 500 b. 450 c. 600 d. 550
In how many ways can 20 distinct frogs be arranged in a row for an experiment when only three frogs can be displayed at a time? A. 4570 B. 7,520 C. 840 D. 5,110 Evaluate √(6^2) A. 120 B. 50 C. 30 D. 15 How many distinct permutations can Maria make from the word MISSISSIPPI? A. 41,214
5 must be thc frst digit, 2 is the second digit, and repetition of digits is allowed? A) 6 B) 8 Ci 4 14.5 must be the first digit, 2 is the last digit, and repetition of digits is not allowed? A) 16 B} 8 D) 2 How many permutations there in the letters of the word HELPING if ING must stay…
A restaurant offers four sizes of pizza, two types of crust, and eight toppings. How many possible combinations of pizza with one topping are there?
Tou Tave 0 peupie Youi ciud Mo Many Woys cdnyou chouse Ftesidem; Secretary? There are 5 colors to choose from, how many unique 3 color flags can be made? You need to pick three people to be in a committee There are 7 people t0 pick frc different committees Gn voumake?
Caterer offers 2 kinds of soup, 2 kinds of meat dish, 1 vegetable dish, and 2 kinds of fish dish. Out of these dishes, the caterer wants to have 100 distinct menu options. How many possible combinations of soup, meat dishes, fish dishes, vegetable dish, and desserts are there? Support your…
Julia cannot remember a 7-character password she created years ago, so she decides to just try all the possibilities until she finds it. The first 2 characters of the password are numerical digits (0-9), and the last 5 characters are letters. both digits and letters can repeat; how many…
A family of 8 can be seated around a circular table with 8 chairs. 7. In how many ways can 368,720 members be seated in a round table? 4,032, 5,040 If a certain four people are seated side by side? 576, 144, 396
Which of the following derives the formula of permutations of objects taken r at a time? P(n,r) = n! / (n-r)! C.P(n) = n! / (n-r)! P(n,r) = n! / (n-r)! P(n,r) = n! / (n-r)! Which solution is the same as P(9,5)? 9 x 5 9 x 8 x 7 x 6 x 5 9 x 8 x 7 x 6 x 5 x 4 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 When…
Different samples of size n-3 can be selected from a population with the following sizes: A. N=5 B. N=15 C. N-7 D. N-13
How many different 4-digit numbers can be formed from the digits 1, 3, 5, 7, and 9 if repetition of digits is allowed? 225, 100, 125, or 625?
In how many ways can 5 learners stand in a circular to play a game? A teacher wants to assign different tasks to her learners. In how many possible ways can she do it? How many distinct permutations of the letters of the word PHILIPPINES are there? Nnm W choose cleaners from 20 learners?
Q3. In the expansion of (2 find the 7th term:
15. Calculate C(20, 7) A. 77 520 B. 77 250 C. 77 025 D. 77 052 Checked and Reviewed by:
On the plane; there are 6 diflerent points (no 3 of them are lying on the sare line) . How many segments can be drawn by joining all the points? Thc School Chess Club has members_ In how may many ways ca 3 members of the club be chosen for the Rules committee?
a. 720 b. 700 c. 36 d. 30 3. In how many ways can 8 people be seated around a circular table if two of them insist in sitting beside each other?
The bowl contains red marbles, yellow marbles, and blue marbles. In how many ways can the balls be selected given each condition? If all the marbles are yellow, how many are there exactly?
Given: n = 5 Solution: Plan;) 0 = 1 P(5,3) = 0.1412.60 (5 - W)
Evolving Permutations and Combinations: In this module, you are expected to solve problems involving permutations and solve problems involving combinations. How many organizations are there? 20.3 How many? 10. How? What I Know: Directions: Encircle the letter of the correct answer: What…
15. There are 4 different Mathematics books, 3 different Arts books, and 5 different History books. In how many ways can the books be arranged on a shelf if the History books are kept together? A. P(12,5) B. P(8,5) C. P(8,5) D. P(5,5) E. P(8,8) P(5,5)
17.. In how many ways can a committee of three be formed from a group of 10 members? A. 480 B. 360 C. 240 D. 120
Spaces available, in how many different ways can this be done? There are only 3. In how many ways can 10 different books be arranged on a shelf?
Text: Determine if the given situation is a Permutation or Combination 10 points Permutation Combination For a survey, students are chosen from a group of 10 students. Pull out 3 coins from my purse that consist of a five-centavo coin, a ten-centavo coin, a peso coin, a five-peso coin, and a…
A closet has 4 shirts, 3 pants, 2 hats and 4 pairs of shoes. How many possible outfits can be made, using one of each kind?
Permutations? 5. Which of the following conditions involves your Facebook account? The arrangement of letters in the password often confuses three students from your class. The order of the winners in the contest is [I II & HI I & HII L,4 & I].
Directions: Write the following problem in Permutation notation: Eric wanted to arrange his collection of books on the bookshelf. He has 10 books. In how many ways can he arrange them if there are only 7 available spaces?
CIRCULAR or BLITHER of these Write your Tell each arrangement is LINEAR; number answer on the space before each 1. Digits in an eight-digit number Plates on the table 3. Horses on carousel
How many different permutations of letters can be made in the word BASKETBALL? 907,200 3,628,800 362,880
In how many ways can girls and boys be arranged in a row so that all three girls are together? If repetition is not allowed, how many three-digit numbers can be formed from the digits 3, 4, 5, 7, 8, and 9? How many of them are even? How many of them are greater than 400? How many of them are…
Great! You have reached this part of the module. Ensure your full understanding of the concepts of permutations and combinations. It is important that you are able to complete each statement below. Fill the blanks with correct words. Permutation is used when order is taken into consideration,…
II. Solve as indicated SHOW SOLUTIONS Find the number of permutations of the letters of each word. (2 points each) MALAKAWAYAN BANABA 2. ANONANG BAKAWAN 3.0 ANTIPOLO
D. If there are 3 men and 3 women in a round table; in how many ways can they be seated if two particular woman must not sit together? Distinguishable and circular permutation
A list of possible judges is composed of seven women and five men. How many different juries can be formed from the list if: the jury consists of four women and three men? the jury consists of two women and four men? the jury consists of five judges with at least one man?
Ashrtey has seven CDs on his desk. In how many ways can he select three CDs? 0.45 I5 Four out of seven students are needed to hand out programs at the drama club performance. In how many ways can the four students be chosen?
How many ways can we arrange the letters A, B, and C?
1) n= 4 Cz 3 4 P & : 4! C4-5).
How many distinguishable ways can you arrange the letters in the word ACCOUNTANCY such that all vowels are together?
The word "ARTICLE" has nine letters. How many permutations and last positions of consonants in the word?
Test V; Find the combination. Choose your answer in the box below and write the letter of your answer in the space provided: 19448 b; 495 C165 d231 e: 300 C(11,8) (25,23) 3. C(17,10) 4. C(22,20) 5. C(12,8)
4 different objects can be arranged in ways
Name: Activity 4 Part 2: Solving Problems Involving Permutations In a group study, women and 3 men sit in a circle. How many ways can this be done if there are no restrictions? 1) Men and women alternate. 2) Alex and Ramela sit together. 3) Alex, Ramela, and Sam sit together. 4) Arlene,…
1) P(11, 4) Answer: P = 7920
Find the value of the indicated term in P. nPc "hint for the answer 206 The average number of adult human bones 232 The number of letters of the longest English word without consonant 352 The atomic number of Calcium in the Periodic Table 4560 The number of island groups in the Philippines 526…
How many line segments can be formed from 6 given points with no three of which are collinear? Given: n = 6, T = 2 Formula: n! / (n - r)! * r! = 6! / (6 - 2)! * 2! = 6! / 4! * 2!
Ikxk < 1,- is of (l + kr) + 2. Given that the binomial expansion 1 - 6r + Ax + ... (a) Find the value of the constant k. Simplest form: Find the value of the constant A, giving your answer in its...
If there are 10 points on a plane, 4 of them are collinear and no other 3 points are collinear, how many lines are formed?
When a pair of dice is rolled, in how many ways can the sum of the two numbers be 7?
Learning Task J: Derive and Find the formula for finding the number of combinations in the following situations: Looking at the beautiful sky of a very peaceful night, Constellation Libra; it has shown six stars, you recognize the distinct points on a plane. How many polygons can be formed? In…
Evaluate 6! + 2! a. 722 b. 622
7.A soloist is auditioning for a point musical play: If she is required to sing any three of the 7 prepared songs, in how many ways can she make her choice? A. 325 B. 320 C.315 D. 310
1. Find the number of distinguishable permutations of the letters in the word PHILIPPINES. 2. Find the number of ways can 6 people be seated in a circular table.
Which of the following is true in the definition of factorial? nl = (n-1) (n-2) (n-3) nl = n(n-1) (n-2) (n-3) nl = (n-1) (n-2) (n-3) 3(2)(1) nl = n(n-1) (n-2) 3(2)(1)(0)
Text: Fn Matching Type: Choose the letter at Column B for the appropriate formula that will give the permutation of the given problem at Column A. Write your answer on a separate sheet of paper: 0/4 Is P = plHl qi 19 I5 i+ ju jOT P = pl rl 9l 19 It '01 S1 How are you today? Did you sleep well…
Dineclons Solve each problem. Show your solution following the Fundamental Counting Principle. Write your answer in the second column. Word Problems: How many 2-digit numbers can be formed from 9 numbered digits if repetition of the digit is not allowed? Answer: How many 4-digit numbers can…
SAQ-1: How do you solve permutation questions/problems? SAQ-2: Is there a need to consider the formula in finding the number of permutations of objects? Why? Let's Practice! (Use separate sheets for your answers.) Activity: Evaluate the following: 54, 91, 104 P(6,6), P(8,3) B. Solve each…
Read each combination value directly from Pascal's Triangle: 5C4 OA = 4 OB = 5 OC = 120 OD = 20
How many ways can a committee of at least 4 people be formed from a group of 6 people?
4!6!/2!5! Simplify your answer as much as possible.
1. How many different ways can 18 questions on a true-false test be answered if a student answers every question? 262484 262254 261654 262144
Algebraically determine the coefficient of m^4n in the expansion of (3m + 2n)^7.
James is choosing a four-digit Passcode for his smartphone. How many different Passcodes are possible? There are ten digits that James can choose from.
How many ways can the letters in the word RIFFRAFF be arranged?
A group of 28 people need to take an elevator to the top floor. The elevator can fit seven. How many ways can they choose a group of 7 to ride the elevator on the first time? 1,213,060 7,104,240 592,020 1,184,040
2. One of the terms in the binomial expansion of (3 + ar);; where a is & constant; is 540+' Find the possible values of a.
A Track and Field relay team consists of 4 team members lined up in order around a track in the 4 x 100 meter relay. How many different line-ups are possible if the 4-man relay team is chosen from among 6 possible team members?
Tina must select and answer in any order two of nine essay questions on a test. In how many ways can she do so?
If all the letters of the word ARRANGE are arranged in all possible ways, in how many of - Words We Will have thc A's not together and also the R's nol together:
1. A group of five students is to be chosen from a 45-member class to represent the class on the student council. How many ways can this be done?
In a room of 5 people, how many different handshakes are possible?
ActivityZ Matching Type: Match Column B with Column A Write the letter of the correct answer: Column B Column A 1. 6Pa A. 40,320 2. BPv B. 24,024 3. :Pa* sP4 C. 720 4. 9P, = 72 D. 120 5. 4! E. 24
Seven red, three green, and five yellow marbles are to be arranged. All the marbles of the same color are not distinguishable from each other. How many different arrangements are possible?
For items no: 1-5, Janna celebrates her 18th birthday. She invited six of her closest friends (3 boys and 3 girls). Find the number of arrangements with the following restrictions: - They are all seated at a round table. - Boys and girls are seated alternately. - All boys sit together. - Four…
3. In how many ways can Myrna arrange 8 potted plants in a row?
Exercise 2. Directions: Solve the following problems on your answer sheet 2. How many ways can you arrange 5 distinct objects taken 3 at a time if repetition is allowed?
LEARNING TASK 3: How many permutations can be made from the letters in the following words: PHILIPPINES, MISSISSIPPI, GULANG, GULANG, ' .(, MATATALINO, IBABANG, IYAM
How many ways can the letters of the word PHOENIX be arranged?
A die and a coin are tossed. How many outcomes are possible?
5. How many four-digit numbers can be formed from the numbers 1, 3, 4, 5, 6, 8, and 9 if repetition of digits is not allowed? A. 720 B. 540 C. 360 D. 840
P(8, r) = 6 720
Error plate number consists of a four-digit number followed by three English alphabet. How many motorcycle plates are possible?
arrange his guests around a dining table? Find the number of different ways that a family of 7 can be seated around a circular table with 7 chairs.
How many two-letter subsets can be made from the set of letters {A, K, O} if order is important?
Evaluate the following: C (4_ C(,3)+C (11,9) C (9,4)-C (9,5) C (13,r) =286 C (n,2)= 56
3. Evaluate: 8P3 336 6720 24 56
Use the Binomial Theorem to prove that (E - o(k))^2k = 3^k
What is 6P4 =? b. 24 d. 360
15 How many eleven- letter patterns can be formed from the letters of the word Mississippi ? A. 11! B. 11! / (4!4!2!) C. (11-1)! D. 11! / (4!3!2!)
2. How many ways are there to seat 6 people around a round table for lunch? 100 120 700 5040
Ben & Jerry's ice cream has 9 different flavors, offer 3 different sizes and you can choose a sugar cone, or a cup. How many outcomes are in the sample space? Just type a number:
Eight students are seated at a round table In how many ways can they be seated if three of them insist on sitting next to each other?
10. How many 4-digit odd numbers can be formed from the digits 1, 2, 3, 4, & 5 if repetition is allowed?
14. How many different quadrilaterals can be formed from 8 non-collinear points on a plane? A. C(8,5) B. P(8,5) C. C(8,4) D. P(8,4)
In a group of 10 people, five Php15,000 prizes will be given. How many ways can the prizes be distributed?
19. Find the number of distinguishable permutations of the letters SWEET. A. 30 B. 60 C. 90
TEST I. Evaluate and simplify the following given. (Write only the answer. Example: 50) 1) 4!
ACTIVITY 2: Permutation and Combination Tell whether a given problem situation involves Permutation or Combination then solve: 13. A bank plans to assign an identification number to each account: Each account number will have five digits, and no digit will be repeated: How many different…
8, If C (n, 4) = 35, what is n? A. 5 B. 6 D. 8
6. From 20 qualified applicants, in how many ways can 8 teacher applicants be chosen?
How many ways can identical pen sets and identical watches be given to the graduates each receives one item?
How many permutations are there in the word BALLOON?
1. Ten points are randomly placed on a circle_ In how many different ways can you form each geometric figure? Show your solution) A Triangle (2 pts) D. Heptagon (2 pts) B Quadrilateral (2 pts) E. Octagon 2 pts) C. Pentagon (2 pts) 2. How many polygons can be formed from & non collinear points…
DJ Cynthia is making a playlist for a radio show. She is trying to decide what 10 songs to play and in what order they should be played.
Use the binomial theorem to answer this question for: (4xy)^2. Show the summation notation equation to express this expansion. x^(-k)y^k * kC(n - k) (c) Using the equation you wrote in part (a), use it to determine the third term of this expansion (show work). Have the coefficient in your…
Name: Directions: Determine the values of n and/or r: (2 pts each) (Written Work) 1. P(n, 2) = 30 2. P(7, r) = 840 3. C(n, 10) = 3C(n, 9) 4. C(13, r) = 286 5. C(n, r) = 4 and P(n, r) = 24
There are 13 female board members and 17 male board members. How many ways are there to make a committee of 16 board members? How many ways are there to make a committee of 16 board members if exactly 6 must be female?
There are 7 runners in & race. How many different ways can the 7 runners finish the race, assuming there are no ties? 49 B 5,040 28
Find the circular permutations of 15 students seated around a circular table. Your 13 friends are sitting at a round table. Find the number of ways they can be arranged. Your mother made 5 side dishes. How many ways can she arrange them at a round table? Find the number of ways that a family of…
3. In how many ways can 5 men and 5 women be seated at a round table if there is no restrictions?
14 In how many ways can two blue marbles and four red marbles be arranged in a row? a 5 b 15 c 20 d 30
For numbers 6-11. Read the situation and answer the following questions: A box of Mrs. Donut contains 6 honey dipped, 6 Bavarians, and 7 chocolate-filled donuts. 6-7. How many ways can 5 Bavarian donuts be selected? a. 5 C d. 8 b. 8 8-9. How many ways can 2 chocolate-filled donuts be…
In a wedding reception, five couples, including the groom and bride, want to have their picture taken: In how many ways can they arrange themselves in a row if couples must stay together?
12. If P(n, r) = 120, which of the following are possible values of n and r? A. n = 6, r = 4 B. n = 7, r = 3 C. n = 6, r = 2 13. In how many ways can Jenny choose three flavors from six flavors of milk tea? A. 20 B. 12 C. 10 D. n = 7, r = 4 D. 120
5) How many 5-digit odd numbers can be formed from the digits 1, 2, 3,4, and without repetition?
Find the number of ways in which 5 people A, B, C, D, and E can be seated at a round table, such that A and B must always sit together, but C and D must not sit together.
Answer the following problems by applying the concepts of permutations. How many emails can be formed from using two English alphabets and four digits if there is no restrictions?
In an All-Area track meet, 271 sprinters enter a 200-meter dash competition. The track has 7 lanes, so only 7 sprinters can compete at a time. At the end of each race, the six non-winners are eliminated, and the winner will compete again in a later race. How many races are needed to determine…
In how many ways can 8 different books be arranged on a shelf? 40,320 8 5760 5040
Evaluate the following: 1.51 2. 3141 3.6121 L (2-4 16-1 (20- 18)' 9. P(6, 31 10. P(3 , 31 7980 120 130 144 #1 #2 #3 #4 #5 #6 #7 #8 #9 #10
From a standard 52-card deck, how many 7-card hands contain all clubs? A hand of 7 clubs can be chosen in ? ways.
How many different 7-digit numbers can be formed from the digits 0, 1, 2, 2, 3, 3 assuming that no number can start with 0? b) How many of these numbers will end in 0?
ACTIVITY 2: Answer the given item completely. Show your solution. (5 points): PERFORMANCE TASK In how many ways can the letters of the word MATHEMATICS be arranged ina row?
C. Solve for the unknown value of n by filling the blank(s): nPz = 12 n! / (n-2)! = 12 n(n-2) = 12 n^2 - 2n = 12 n^2 - 2n - 12 = 0 (n-4)(n+3) = 0 n = 4 n = -3
MULTIPLICATION COUNTING RULE 4. Your school offers two English classes, three math classes and three history classes. You want to take one of each class. How many different ways are there to organize your schedule? Solution:
Answer the following questions correctly and you will get a summoning scroll and 10K coins. 1/10 Lucy wants to wear different clothes every day. She has dresses, pairs of shoes, and pairs of earrings. Lucy could choose a dress, a pair of shoes, and a pair of earrings every day. However, some…
Sample space, probability, permutation, d. sample space. 5. In how many ways can you arrange 8 books on a shelf if only 5 books can fit at a time? 6,920 ways. b. 6,820 ways. 6,720 ways. 6,420 ways. 6. It is a numerical value that describes the likelihood that an event will happen or not.
Screenshot the problem and scan it with the Gauthmath app; enter the answer, and earn 200 Coins. In an All-Area track meet, 271 sprinters enter a 200-meter dash competition. The track has 7 lanes, so only sprinters can compete at a time. At the end of each race, the six non-winners are…
4. Using the letters of the word INTERMITTENT how many 12-letter arrangements can be formed: without restrictions (2 marks) if each word begins with T and ends with N (2 marks) if the 4 T's are together (2 marks) if each word begins with 2 T's (2 marks) if each word begins with exactly 2 T's (2…
The coefficients in the expansion of (x+y) can be found using a row of Pascal's triangle.
OE "0 How many three-digit numbers composed of different numbers can be formed from 0, 2,3, 5, and 67
There are 26 boys and 28 girls in a rugby club. Sophia selects two girls from the club. How many ways of choosing are there?
3 1 1 3 0 64, { # $ # ; 2 : L 6 1 C
Determine the 20"h term in the expansion of '-y)
Nov 1st, Students from the 17-member assembly committee of 14 principals would like to know how many different committees can be chosen for the student council.
Use the Binomial Theorem to expand the expression (x+y5) (Simplify your answer )
If automobile license plates consist of four letters followed by one digit bow many different possible license plates are possible if letters ad numbers may be repeated? Select One 676,000 45.697.600 456.976.000 1.757.600 None of These
What is the value of the 6th term of the expansion (a + b)^9? 0 84a * 66 0 844663 126a^4 05 1260564
A In R, what does n stand for?
Question 10 (2 points) Algebraically determine the coefficient of mn in the expansion of (3m + 2n)
are greater than 50 million can be created many even eight digit numbers that 7 How 0,2,2,3,4,5,9, 9 ? using all the digits
12 In how many ways could 15 different books be divided equally among 3 people?
Expand (x + 5) 4 using Pascal's triangle (x+5)4 (Simplify your answer )
40 people are randomly selected and the accuracy of their wristwatches is checked, with positive errors representing watches that are ahead of the correct time and negative errors representing watches that are behind the correct time. The 40 values have a mean of 99 sec and a standard deviation…
Find the standard deviation of the following data set. Assume the data set is a sample. Round your answer to the nearest hundredth, if necessary. 35,70,31,37,65,38,38,44,43,43,68
A researcher randomly purchases several different kits of a popular building toy. The following table shows the number of pieces in each kit in the sample. Find the median of the data. Building Toy Pieces 160 45 265 350 350 45 104 296 265 109 170 208
Grocery Retailers Association of South Africa (GRASA) believes that the average amount spent on groceries by Cape Town shoppers on each visit to a supermarket is R175. To test this belief, the association commissioned Market Research e-Afrika to conduct a survey among a random sample of 360…
2.1 Bertino et al. (A-3) conducted a study to examine prospectively collecied data on gentamicin in pharmacokinetics in three populations over 18 years of age: patients with acute leukemia, patients with other nonleukemic malignancies, and patients with no underlying malignancy or…
find the critical valve zc that corresponds to a 90% confidence level.
Suppose the correlation between two variables is r = 0.19. What is the new correlation if 0.23 is added to all values of the x-variable, every value of the y-variable is doubled, and the two variables are interchanged?
A plant manager wishes to determine the difference in number of accidents per day between two departments. She wants to be 90% certain of the difference in daily averages to within 0.25 accidents per day. Assume standard deviations of 0.8 and 0.5 accidents per day in the two departments,…
Taxicabs in a metropolitan area are driven an average of 75,000 miles per year with a standard deviation of 12,000 miles. What is the probability that a randomly selected cab has been driven less than 100,000 miles if it is known that it has been driven over 80,000 miles? Assume a normal…
Suppose the probability that a person picked at random has lung cancer is 0.035 and the probability that the person both has lung cancer and is a heavy smoker is 0.014. Given that someone picked at random has lung cancer, what is the probability that the person is a heavy smoker?
Which of the following is not true about t-distributions? A. There are different t-distributions for different values of df (degrees of freedom). B. t-distributions are bell-shaped and symmetric. C. t-distributions always have mean 0 and standard deviation 1. D. t-distributions are more…
To conduct a survey of which long distance carriers are used in a particular locality, a researcher opens a telephone book to a random page, closes his eyes, puts his finger down on the page, and then calls the next 75 names. Which of the following is a correct statement? A. The procedure…
Following is a histogram of ages of people applying for a particular high school teaching position. Which of the following is a correct statement? A. The median age is between 24 and 25. B. The mean age is between 22 and 23. C. The mean age is greater than the median age. D. More…
A local school has seven math teachers and seven English teachers. When comparing their mean salaries, which of the following is most appropriate? A. A two-sample z-test of population means B. A two-sample t-test of population means C. A one-sample z-test on a set of differences D. A…
Which of the following is a false statement about simple random samples? A. A sample must be reasonably large to be properly considered a simple random sample. B. Inspection of a sample will give no indication of whether or not it is a simple random sample. C. Attributes of a simple random…
Suppose that the regression line for a set of data, y= 7x + b, passes through the point (-2, 4). If and are the sample means of the x- and y-values, respectively, then y=
To study the effect of alcohol on reaction time, subjects were randomly selected and given three beers to consume. Their reaction time to a simple stimulus was measured before and after drinking the alcohol. Which of the following is a correct statement? A. This study was an observational…
What is a placebo? A. A method of selection B. An experimental treatment C. A control treatment D. A parameter E. A statistic
The graph below shows cumulative proportions plotted against numbers of employees working in mid-sized retail establishments. What is the approximate interquartile range? A. 18 B. 35 C. 57 D. 68 E. 75
The label on a package of cords claims that the breaking strength of a cord is 3.5 pounds, but a hardware store owner believes the real value is less. She plans to test 36 such cords; if their mean breaking strength is less than 3.25 pounds, she will reject the claim on the label. If the…
Suppose that 60% of a particular electronic part last over 3 years, while 70% last less than 6 years. Assuming a normal distribution, what are the mean and standard deviation with regard to length of life of these parts? A. μ = 3.677, σ = 3.561 B. μ = 3.977, σ = 3.861 C. μ = 4.177, σ =…
Consider a hypothesis test with H0 : μ = 70 and Ha : μ < 70. Which of the following choices of significance level and sample size results in the greatest power of the test when μ = 65? A. α = 0.05, n = 15 B. α = 0.01, n = 15 C. α = 0.05, n = 30 D. α = 0.01, n = 30 E. There is no way of…
In comparing the life expectancies of two models of refrigerators, the average years before complete breakdown of 10 model A refrigerators is compared with that of 15 model B refrigerators. The 90% confidence interval estimate of the difference is (6, 12). Which of the following is the most…
The parallel boxplots below show monthly rainfall summaries for Liberia, West Africa. Which of the following months has the least variability as measured by interquartile range? A. January B. February C. March D. May E. December
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