Home
Ask directory
Intro Stats / AP Statistics
August 2022
9

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

Select Question

August 9 of 2022

9. Evaluate: C (7,4) A. 5 B. 15 C.25 D. 35 10. The first ten letters of the English alphabet are to be used by a certain company &s employee codes in sets of five . Find the number of combinations_ A. 25 B. 225 C. 252 D. 552

2. In how many ways can people be seated around a circular table? n-4, P= (4-1)! 31 (31(21(1) 6 waye

How many quadrilaterals can be formed from 10 points?

360 B. 720 1440 D. 5040 2. How many 7-letter words can we make with the letters in the word 'MATHEMATICS'? A. 7,920 B. 15,840 C. 31,680 D. 63,360 3. At the grocery section, Kyvhan wanted to select 2 diapers, 2 milks, 3 shampoos.

How many different license plates are possible if Kentucky uses three letters followed by four digits?

Attempt all the questions. Rewrite with absolute value |x| < 3 formed from the integers: 0, 1, 2, 3. How many different digit numbers can be 4, 5, or 2?

5. HOW MANY TWO DIFFERENT DIGITS CAN BE FORMED BY CHOOSING FROM 1, 2, 3, AND 4? A. 16 B. 12 C. 10 D. 7

Solve for n. P(n,2) P(n,3) = 720 P(n,n) = 5040 P(n,6) = 1 * P(n,5) 30 * P(5,4) = 80 * 6

A bag contains balls of five different colours Two are red; three are blue, ten are white, four are green and three are black. Balls are taken from the bag without looking; and not returned . What is the smallest number of balls that should be taken from the bag to be sure that two balls of the…

5. Using the digits 0, 1, 2, 3, 5, 7, 8, how many three-digit numbers can be formed if repetitions are not permitted? A 120 B 216 C 240 D 180

4 1o 31+4 6 4-(5I+ 31)

5. Using the digits 0, 1, 2, 3, 5, 7, 8, how many three-digit numbera can be formed if repetitions are not permitted? A 120 B. 216 C.240 D. 180 6. There are 4 trails that lead to a scout camp on a hill, In how many ways can a scout go to the camp and go down by going up one trail and down by a…

Use Pascal's Triangle to expand (x + 2)5

I took a 10-item Mathematics problem-solving test; now many guys can you lead! Problems solve? 252 B 254 256 D_258 how many ways can a committee of 5 be formed from juniors and seniors? (The committee must have seniors) 350 B. 355 360 386

What is the distinguishable permutation of the letters of the word EVEN?

The class consists of 10 boys and 15 girls. 4 How many such options for student selection Are there 3 boys and 1 girl in each version?

14. Which is true about the two situations? 1 Selecting the fruits in making fruit salad. I The password of the safe box is 736. Uv" < 1 ~sao 25 (^ 6,1 < e6 <O 0 , AS Both situations are permutations because order is important. B. Both situations are combinations because order is not important.…

16 VOJu3d How many different words can be formed with the letters of the word 'FACTORIAL' such that the vowels always come together?

A 3-letter code is created using the letters from the word COLUMBIA. How many different 3-letter codes can be created? 40,320 120 6,720 336 56

Evaluate (show all your work): 6.) 61 9.) 5! 21 7.) 91 10.) 10! 81 8.) 101

A. Find the number of permutation of letters of each word. 1. BASKETBALL 2. DIFFERENT 3. STATISTICS 4. ACCEPTANCE 5. LEARNING

Solve the following problem: Can you list all possible arrangements of the letters RED?

6. 8C3 + 6C1 7. 8C2 - 8C6 8, 11C4 3C3 9. 12C8 / 5C4 10. 7C2 x 6C3

2) Find the middle term(s) in the given expansions! a b)

16. In how many ways can a committee of 7 students be chosen from 9 juniors and 9 seniors if there must be 4 seniors in the committee? A. 10,584 B. 1,764 C. 210 D. 84 Jane wants to solve a system.

A seven-character insurance account number must be five letters of the alphabet followed by a two-digit number. How many different addresses of this kind are possible? Both letters and numbers are without repetition.

How many ways are Inara Vonckag Ieha arrangements out of the word DISCOVERY?

Use the binomial theorem to expand the polynomial (2x 3y)4 . Upload an image of your answer when you are finished:

Problem 1: In how many ways can in & row? we arange different fruits if we want t0 arrange it 2 Keyword: Permutation Combination Answer: Type of Permutation or Combination Answer: Substitute: Value of Formula: Simplify and Solve: Conclusion:

How many two digit numbers can YoU make using the digit cards? 7 0 2

bukjecl aie KEpl [Uyeltiei" "In how many ways can 6 students be seated in a row of 6 seats if 2 of the students insist on sitting beside each other?" "Suppose you are the owner of a sari-sari store and you want to put 12 pieces of canned goods in a row on the shelf. If there are 3…

B Problem solving Read and analyze the following situations then, answer the questions that follows. A certain password consists of 3 different letters of the alphabet where each letter I5 used only once. How many different possible passwords are there?

How many 3-digit numbers can be formed (only using the digits 0-9) if all the numbers formed are less than 700?

Find the coefficient of 139y^2 in the expansion of (x + 2y)^15. The coefficient of 239y^12 is 7557296947200.

9. How many ways can you arrange the 5 chairs in a row? a. 120 b. 72 c. 50 d. 210

8) How many ways can JANE, LORNA, JAM, IAN, and TRISH be seated around a table such that Jam and Ian never sit together? 12 C. 24 9) @raacbuffet, there are 10 different appetizers from which to choose. The appetizers are arranged on a revolving tray. 345,220 How many ways…

How can a baseball team manager align nine players in the lineup? 362,880 23,800 d. 1,818 Consider the word PEPPERS. How many unique arrangements can be made with these letters? 218 420 520 230 How many ways can yellow, red, and green balls be arranged in a row? 18,224 23,550 26,920 27,720 10.…

Find the number of different arrangements of the set of the following six letters: 0, 2, k, c, +, ?. A circle has 10 randomly placed points. In how many ways can you form each polygon listed below? Triangle, Rectangle.

What formula is used to determine the number of arrangements of objects in a circle? C.(n-1)! D (n-1)! #Ps= 6720, what is the value of n? 70 8 A family is being arranged in a line for a group.

LEARNERS ACTIVITY: Solving Problems involving Permutations and Combinations ACTIVITY Directions: Answer the following: The first number is done for you. Express the following product in simplest factorial form: 9!10 Answer: 10!15 [4!3 - 1!8] / [7!5!4!3!2!] Express the following factorial…

26. If n is a positive integer, show that âˆš(n^2 + 4n) can be expressed as (n + 2) using the Binomial Theorem.

Match Column A with the correct expression in Column B. How many committees with five accountants and three lawyers can be formed from a selection of six accountants and eight lawyers? Determine the number of different permutations of two of the five vowels a, e, i, and u. C(6,2) P(5,2) Find…

How many ways can the letters of the word "MATHEMATICS" be arranged? Keep Trying: How many three-digit even numbers can be formed with the digits 2, 4, and 8?

Three-digit numbers divisible by 3 are to be formed using any of the digits 0, 1, 3, 5, and 9. How many of this kind can be formed such that digits cannot be repeated?

Determine whether each of the followng is True or False 1.) 10! 10 x 9 x 8! TRUE FALSE 2.) 6! x 31 18! TRUE FALSE

9. Find the unknown in P(7,4) = B. 840 B. 1680 C. 10,080 D. 40,320

Pick 3 items from 10 in any order, where n = 10, r = 3. The total number of ways of making the selection are

1. C(7,5) = 21 2. C(6, r) = 20 3. C(10, 4) = 210 4. C(n, 3) = 35 5. C(r, 2) = 28

10. C (14, 10) =

12. Seven Grade 10 students, boys and girls, decided to have their group study at Mathematics Park. Only boys must sit beside each other. What is the possible arrangement of them around a circular table? Which of the following is the possible arrangement of 8 beads in a bracelet? …

Which of the following situations illustrates combination? Arranging books on a shelf. Assigning telephone numbers at home. Choosing household chores to do after class. Selecting posters to hang on the walls of your room.

In how many ways can 11 different books be arranged on a shelf? * 39,961,800 39,916,080 39,691,800 39,916,800

The number of permutations of n things taken at a time is equal to nPr.

A circle: How many quadrilaterals can be formed using any 4 of the seven points marked on the circle? Options: A. 20 B. 35 C. 70 D. 15

16, In How many ways can people arrange themselves in row for picture taking? 17, In how many ways can bicycles be parked If there are avallable parking spaces?

Text: General Direction: Read each item carefully. Write the letter of the best answer on the space provided. Explain your answer for each item by showing your solutions. Use an extra sheet of paper for the solutions. Quarter 3 Week 1: ILLUSTRATING PERMUTATION SCORE: The possible race results…

Letters digits. How many licenses a license #ok must have. Three are possible.

25*. How many even 3-digit positive integers can be written using the digits 1, 2, 4, 7, and 8?

if P(7, x) = 7!/3!, what is x? A. 8 B. 6 C. 4 D. 2

7. How many different ways can the letters of the word BANANA be arranged? A. 5 B. 6 C. 50 D. 60 In a family of 7, how many arrangements can be done during a circular family dinner? A. 207 B. 720 C. 5,004 D. 5,040 11. In how many ways…

Let N be the number of elimination games. 1010*9*8*7*6x514232212 = 101N - C(10, J)21(10-7)1 2421

9. C (n, 4) = 10. C (11, r) =

C(n,r) = 20 points (n-r)lr! Find the value of the following, (Show your solution. 2 pts each) C(7,2) C(5,4) C(24, 20) * C(10, 6) C(8,21) * C(7,51)

A committee of 3 people is to be chosen from 5 women and 7 men. Find the number of different committees that can be chosen if there are more women than men.

Find the number of three-digit numbers that can be written using the digits (4, 2, 3) without repetition of digits.

A bookshelf has n diffcrent Algebra books and thrce different Geomet books_ If there are 5 040 ways to arrange the books on the shelf; many Algebra books are on the bookshelf? B. 5 D. 7 Use this situation for items 10 12 Find the number of differ arrangements of the set of the seven letters…

If you are playing SCRABBLE and there are 7 distinct letters on your wooden tiles, how many "words" can you form using all these letters? * 6,720 5,040 5,207 6,040

There are three dials on a combination lock. Each dial can be set to one of the numbers 1, 2, 3, 4, 5 The three digit number 514 is one way the dials can be set as shown in the diagram. a) Work out the number of different three digit numbers that can be set for the combination lock. (2) b) How…

Match the correct value 10 points 24 121 120 41

There are 8 books on a shelf. In how many ways can you select 4 books. A) 10 C) 50 B) 30 D) 70.

For these, if each signal uses 3 flags? In how many ways can 5 bicycles be parked if there are available parking spaces? Elc and different music books.

Test V. EVALUATING: Evaluate the following permutations. Write your answers on a separate sheet of 'pad paper. 4P2, 4P3, 4C3.

12. If we have a total of elements, the integer (1_ 7). Now, how many unique sequences of three elements (2, 5, 7) exist from this set? In the given problem, which of the following formulas should be used in solving the problem? A. nPr B. nCr C. nCr D. nPk

In how many ways can 6 keys be arranged in a key ring? 15 30 45 60

Em found out that she has 10 bills in her wallet, 4 are one thousand-peso bills, 3 are five hundred-peso bills and 3 are one hundred-peso bills. How many permutations are there?

Ten people posing for a picture. No three points are collinear. Creating triangles from a drawn 5-sided polygon. Diagonals that can be found. Determining the total number of different ways to arrange the top three awardees. Placing books on a shelf. Cards formed from a standard deck of 52…

Answer the following problems considering that repetition is allowed in the space provided before each number. The first situation is: A young lady decided to choose 2 flavors from 5 of her favorite flavors of ice cream to be served on her 5th birthday. How many combinations are…

Find the number of distinguishable permutations of the word EDUCATED. a. 1,680 b. 1,080 c. 20,160 d. 40,320 Peter Pan has pairs of shoes, pairs of pants, and 14 t-shirts. How many possibilities can he have?

2. Calculate P(11,4) A. 55440 B. 7920 C. 2520 D. 990

Application: Try to work on this. Give the combination of each of the following, given the number of objects (n) and the number of objects taken at a time (r). The first number is done for you: number of objects (n) = 5, number of objects taken at a time (r) = 3. c(n,r) = n! / (r!(n-r)!) …

7. In how many ways can 5 boys and 5 girls be arranged in a row for picture taking if: a) all boys are together? b) boys and girls are arranged alternately?

III: Assessment Application/Outputs Directions Choose the letter of the correct answer. It is a selection of objects from a set. A. combination B. differentiation C. permutation D. distinction Which of the following situations illustrates a combination? arranging books on a shelf drawing…

How many different ways can the 8 persons be seated in a circular table? A. 5,040 B. 5,220 C. 5,440 D. 5,520

P (8, 3) =

How many chords can be formed from the circumference of the circle? If there are even points formed on the circumference. How many different 10-member committees can be formed from the senators of the country?

Write P if the situation/problem is involving permutation and N if Not Write the corresponding notation if the problem involves permutation. 1 , Ten runners join a race: In how many possible ways can they be arranged a8 sklirst, second, and third placers?

From a class with 40 students, 8 students will be chosen to join the science field trip. In how many ways can the students be chosen? Given: n- Formula: C(n,r) = n! / (r!(n-r)!) Solution:

6. In how many ways can the letters of the word ""CLASSICAL"" be arranged? a. 362,880 b. 22,680 c. 360 d. 72

Find the value of P(5,4)+ C(5,1) B. 5 C. 6 D. 125

And YELLOW, where three marbles have to be kept one upon another, a game has to be made from marbles of three colors: RED, GREEN, and another. In how many ways can these marbles be arranged? Select one.

DIRECTION: Provide the answer to the following given situation. Justify the outcome of your solution: In the player's jersey, there are 2-digit numbers. How many different numbers can we get? Choose.

Find the number of different ways that an instructor can choose 3 students from a class of 17 students for a field trip.

In how many ways can all the letters of the word "MONTREAL" be arranged if the letters R, E, A, and L must appear in order as the word REAL in all arrangements?

In how many ways can the letters of the word SWIFTNESS be arranged if all the letters are used and the vowels are kept together?

A combination lock like the one shown has three dials. Each of the dials has numbers ranging from 1 to 8 How many different combinations are possible with the lock? 343 combinations 48 combinations 512 combinations 24 combinations

From a group of 12 student representatives, 6 will be chosen to work on a committee: How many committees of 6 are possible if Sally & Sam must be on the committee?

Question 2 To choose the three players fairly; Coach Bennet decides t0 ser up a free throw contest The three players who make the most consecutive free throws will get to g0 to the summer basketball clinic: Part A Question How many different orders of top-three finishers are possible? Drag the…

Determine whether the situation represents a permutation or combination; then solve How many ways can a president; vice president; and treasurer be elected from a group of 20 students? Sample Answer: 1,234 59,280 6,840 1,140 1,150 None of the Above

There are 20 horses in the Kentucky Derby. How many different ways can the horses finish 1st, 2nd and 3rd place? 60 6,840 1,140 20

How many odd four-digit numbers can be formed from the digits 1, 17. 2 3 and 42 Write the possible odd numbers.

What is nif -448x^3 appears in the expansion of (x + 2y)^3.

From 4 red, 5 green, and 6 black ballpoint pens, how many selections of 9 ballpoint pens are possible if 3 of each color are to be selected? Clue: 1st activity n=4, r=3; 2nd activity n=5, r=3; 3rd activity n=6, r=3.

How many different paths will spell the word CASH using the diagram below?

Find the number of possibilities using permutations or combinations The student body of 10 students wants to elect a president vice president secretary,_ and treasurer:

When we randomly select a permutation of {1,2}, what is the probability that 1 immediately precedes 2? Given that n = 8, what is the probability? Write your answers in decimal form and round off to the nearest hundredths.

2 . How many different 3-digit numbers can be formed from 0, 1, 4, 6, and 8 if no repetition is allowed? b. repetition is allowed? repetition is allowed but all numbers formed are odd? repetition is allowed but all numbers formed are even? 240

25. How many different arrangements of letters can you make from the word "TENNESSEE"? 362 880 3 780 181 440 90 720

Choosing books from a set of books is an example of combination, differentiation, integration. When evaluated, what is the value of C(6)? 48 permutation.

Title: "Permutations and the Fundamental Principle of Counting" Fundamental Principle of Counting (FPCI) states that an activity can be done in n ways; if one activity can be done in n1 ways and another activity can be done in n2 ways, then the activities can be done simultaneously in n1 * n2…

Find the number of permutations of the letters in the word BOOK. a. P = 4! / (4-2)! = 12 b. P = 4! / 2! = 12 c. P (4-2) ! = 2! = 2 d. = 4! / 2!1!1! = 2

Evaluate: 4. 12! A. 479,100,600 B. 479,101,600 C. 479,110,600 D. 479,001,600

What is the coefficient of x^7 in the expansion of (x + y)^12?

2. Six actors and eight actresses are available for a play that requires 4 males and 3 females. How many different cast lists are there? A. 120, 960 B. 40, 320 C. 20, 160 D. 576

q ~o number of arrangements in a row of 7 objects taken 2 at a time Er ` . | 1 [ 'P '1 . ' , . ( ( JE + uax81 swalqo 0T JO MOI â‚¬ UJ SJUJU3BuEIJe JO Iaqunu a time 6 7 ZI ~o fOL J8 9 uaxe} 81231q0 8 jo

Match each expression in column to its corresponding expression in column 2 nPz 3.nPn nPo 5.nl 6. nPs b. n(n-1)(n-2) / (2)(1) 3n! d:n n^n _ n t.nl

For number 3-4: In how many ways can a group of 7 persons arrange themselves? Your answer 3. In a row of 7 seats? 2 points 40,320 5,040 720 120 Around a circular table? 2 points 40,320 5,040 720 120

3. Five Ladies apply for 3 saleslady positions. In how many ways can These position be filled by the lady applicant

The manager at Dunder Mifflin needs to send off their 6 salespeople and 5 warehouse workers on a sales call. How many combinations of salespeople and warehouse workers are there? Review Pascal's triangle here: 462 150 Click Submit to complete this assessment. Question 6 of 6 Save and Submit

Which of the following is the permutation of 10 objects taken 2 at a time?

How many permutations can be made from the letters of the word VACCINATION? 2,494,800 79,833,600 453,600 55,440

The number of ways to arrange 5 people in a row out of a class of 8 people is

FC6 Ibub 1 V8 Ebp? Boo? Sgcb-28 Jbcb _ 8o8 Pa Sbe? 1) RCI- gcI gU I ZC IbcL 5bA fb4R goo? Sgcr :Jb Rgo8 21 Xopk gcL:8 1 8C4.3c2 ~bCb @ * goo 8 24}l Roo gc5 . RCL 806 Tcb JbCb I6ZX Vb Roo? RoR gckel 80 =8} P What does "C" in 8C6 for no: 1 mean and how come it is equal to 28? dont get it. Can…

If a group of 5 people participate in a pie eating contest, how many ways can 1st, 2nd, and 3rd place be awarded? * 6 ways 30 ways 12 ways 60 ways 720 ways None of the above.

4. In how many ways can five people sit at a round table if three of them insist on sitting next to each other?

In how many ways can 12 members of a varsity volleyball team be chosen from 30 persons who tried out? 86 480 325 86 493 225 86 590 445 86 370 665

70 Il "'0+8 iiu Jo anjBA aq1 SI JEYA `Sâ‚¬ = ') JI

In how many ways can 9 runners finish a race in first, second, or third place?

In how many ways can 8 women be arranged in a straight line? 40, 320 10, 260 5, 040 24, 240

Consider the set of numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). How many digit codes can be formed? The code may not contain repeated characters. If the code may not contain repeated digits, different codes can be formed.

How many selections can be made if a committee of 9 people is to be formed from a population of 16 people, but Kiana, Sham, and Yanika must be on the committee?

Copy and solve in a short bond paper A_ Evaluate the following P(8,5) 1. 312! 2. P(4,4) 3. P(6,3)

Determine the number of possible sample of the following if the sample size is n = 3 use the combination formula: N = 20 O a. 140 O b. 2140 O c. 1140 O d. 111400

To win the trifecta you must pick the first, second and third place winners for Ihe race_ If 10 horses are racing; how many different outcomes are there for the trifecta? 720 3,628,800 120 1000 none of the above

2. Find the number of permutations for arranging the letters S, C, I, E, N, C, E in a row.

16. You are setting the combination in a four-digit lock: You want to use the numbers 1 2 3 4 but don't care what order they are in. Permutation, 24 Combination; 24 C. Permutation; Combination, 1

A Math varsity coach is selecting two members to compete in an upcoming Math competition through elimination: The top scorer will be the Primary Competitor and the second top scorer will be the Secondary Competitor. Five members - Thea, LJ, Anthony, Joyce, and Xander - are vying for the spots.…

Which of the following statements is true? a. Arrangement is important in permutation. b. In combination, arrangement is not important. c. Combination is permutation divided by r. d. Information is incomplete. e. iii only except iv. f. iv.

3. In how many ways can the letters in the word "Missouri" be arranged?

Permutation Combination #diger Evolcnnu oui Fdulon Ten Grade 10 students are chosen from eighteen to be members of the Grade 10 Assembly.

How many different signals can be made by arranging 9 banners in a line if 4 banners are red, 3 are white and the rest are blue?

Plates of private cars have 3 letters followed by 4 numbers if letter and number cannot be repeated; how many can be made?

In how many ways can you arrange 6 Mathematics books, 3 Science books, and 4 English books on a shelf such that books of the same subject are kept together? In a panel of 4 members, they will be selected from S men and $ women. In how many ways can 2 of the panelists be men and the other two be…

How many six-digit numbers can be formed from the digits 1, 2, 3, 5, and 6 if repetitions are allowed? A. 702 B. 720 C. 46,656 D. 46,665

Use the formula for nCr to evaluate the given expression: 15C12 * 7C6. 15C12 = 15! / (12! * (15-12)!) = 15! / (12! * 3!) = (15 * 14 * 13) / (3 * 2 * 1) = 455. 7C6 = 7! / (6! * (7-6)!) = 7! / (6! * 1!) = 7. Therefore, the expression evaluates to 455 * 7 = 3185.

How many ways can you arrange a blue ball, a red ball a black and a yellow ball in a row? 100 120 24 60

There are 6 ways that persons can be seated at a round table. This example of Non-permutation Permutation 9/ deleting a single B. Circular permutation Permutation of non-distinct Objects

Activity 2: FACTORIAL NOTATION Evaluate each of the following examples: 7! = 7.6.5.4.3.2.1 = 5,040 10! = 10.9.8.7.6.5.4.3.2.1 = 3,628,800 Remember: n! = n(n-1)(n-2)...(3)(2)(1), where n is a positive integer; 0! = 1 n! is read as "n factorial" 2^4 = 2.2.2.2 = 16 3(11 - 8)! = 3.3.2.1 = 18 5^2 =…

Combine: Direction; Match Column with the correct number illustrating combination Column Write Letter that corresponds to the beet 2B"Ce Column Column How Many Ways choose two Cotes from Orange yellow_ Blue green, How many times table tennis tournament with participating [Cams namely Team _…

Column A permutation with repeated elements G-t (n- nl nInz!na nl nPr circular permutation circular permutation taken a few at a time D. permutation of objects taken a few at a time E. permutation of objects taken all at a time

II: How many different ways can the letters of each word be arranged? Show your solution. (15 points) 1_ PROBABILITY 2. MISSISSIPPI 3. REARRANGE

4. Evaluate: P(7, 5) A. 21 B. 35 C. 250 D. 2520

A close friend invited Czairyn to her birthday party. Czairyn has 4 new blouses (stripes, with ruffles, long-sleeved, and sleeveless) and 3 skirts (red, pink, and black) in her closet reserved for such occasions. Assuming that any skirt can be paired with any blouse, in how many ways can…

From a group of four men and seven women, six are arranged in a row. How many different arrangements are there with each of the following properties? 1. The first three people in the row are men, and the second three are women. 2. Men and women alternate, with the first person in the row being…

How many five-digit numbers with different digits are there if the first and second digits are even?

There are 10 members of a club. How many different 3 member committees can you have?

Use Pascal's triangle to expand (a + 2b). Show work. (TA CI) Row 0: 1 Row 1: 1 1 Row 2: 1 2 1 Row 3: 1 3 3 1 Row 4: 1 4 6 4 1

3. How many distinct permutations can be made from the letters of the word " INDEPENDENCE"? n=12, N=3, D=2, E=4

Iow many ways can 6 boys and 6 girls be seated at & round table if: particular girls must sit together

3. How many 5-letter permutations can be formed from the letters in the word ANCHOVIES? a. 1680 b. 3 024 c. 6720 d. 15 120

Write down the general term in the binomial expansion of (3x).

Use the Binomial expansion of (1 + 2x)20 to evaluate 1.000224, correct t0 /2 decima places

At a used car lot; 9 different car models are to be parked close to the street for easy viewing; but there is only space for 5 cars. How many ways can 5 of the 9 cars be parked in a row? Show your work t receive full marks.

A, ^, 7, and Hi is 90ring one file letter. May 0 of ways face could row find the total number 2w a do miss.

ABSOLUTELY RIGHT A. Direction: Use Pascal's triangle to find the expansion of the following binomials. (2 points each) 1. (x + y)^2 Given: n = 2 Expanded form: x^2 + 2xy + y^2 2. (x - y)^2 Given: n = 2 Expanded form: x^2 - 2xy + y^2 3. (x - 3y)^2 Given: n = 2 Expanded form: x^2 - 6xy +…

Beginning? Make an organized list. 2. A baseball team won two out of their last four games. In how many different orders could they have two wins and two losses in four games? Make a table and look for a pattern.

2 How many permutations of the letters in the word CANADA do not begin with an A?

Use the binomial theorem to find the values of the following: VI,001 correct to six decimal places. [2 Marks]

Decide numbers can be formed if each number starts with 27 and no digit 25. How many 6-digit numbers appear more than once? c 213 127 200 680 70 b 296 010 determined by & points, no three of which are collinear?

Grace is making a movie and needs to cast some actors. There are 3 actors interested in playing the female lead role, and 6 actors interested in playing the male lead role How many different ways can Grace cast the film?

Question 5 I1 Points Out of fifty runners in a race, we want to know how many ways different runners can come in first, second, third, and fourth place. Calculate the number of ways that fifty runners can finish in first, second, third, and fourth places. Fill in the blanks below with the…

A four-letter code is to be formed using four of these cards: (a) Find the number of different four-letter codes that can be formed. (b) Find the number of different four-letter codes which end with a consonant.

Four different colored flags can be hung make coded signal How Many signals if & signal consists of the display of one more flags? be made

A basketball coach will choose 5 players from a group of 8 players to start the next game. How many different groups of starting players are possible?

How many 5-digit numbers can be created using the digits 2, 3, 5, 7, and 8 without repeating any digits within that 5-digit number?

23.) How many 3 digit even number can be formed from set {1,2,3,4,5} without repetition? 10 24 50 60

Alexander is designing a new board game and is trying to figure out all the possible outcomes. How many different possible outcomes are there if he flips a coin and rolls a fair die in the shape of a cube that has six sides labeled 1 to 6?

Find the number of ways for 4-digit even numbers greater than 4000 to be formed by using digits 2, 3, 4, 5, 6, and without repetition.

Find the following terms of the Fibonacci sequence by using the Binet's formula: Show your solution/process to get the answer; 5 points each. Item No solution, no points. 50th term 70th term

Show that âˆš(nCr) = âˆš(n! / (r! * (n-r)!)) Note: nCr represents the combination of n items taken r at a time. r!(n-r)! represents the product of r factorial and (n-r) factorial.

The diagram shows five cards with letters as shown: 4) Diagram: Find the total number of ways of arranging all cards in a row. 6) Find the number of arrangements such that letter E and A must be adjacent to each other:

17"Cr "D-"+ 'D1-" that Show

How many distinct permutations can be formed from all the letters of the word sociological?

In a classroom, there are 23 girls and 25 boys. The class is to elect a President, Vice President, and 2 Treasurers. What is the probability that if students were elected at random, all three positions were filled by girls? 2C2: 2P3 / 25C2: 25P3

Activity I: LET'S SOLVE THIS! Find the number of three-digit numbers that can be written using the digits from the set {1, 3, 5}, assuming repeated digits are not allowed. Answer: 6 (135, 153, 315, 351, 513, 531) A box contains 3 balls: red, white, and blue, respectively. If they are identical…

In how many different ways can 7 potted plants be arranged in a row? 720 210 5 040 2 520

Direction: Fill in the blanks with the correct letters/KuSwec A. You have to create your 4-pin code on your cellphone, you can use the letters M-A-T-H. Continue the pattern for your pin code: MATH, MAHT, MTHA, MTAH, MHAT, MHTA, ATHM, THMA, HMAT.

Find the coefficient of the t4 term in the expansion of (4t S 3)5

Use Binomial Theorem to show that (6 + 14) is divisible by 10.

The number of different orders of yerticu taken at a the actual number combination? Run 1 P(4,31). What

Although Megan is interested in seeing the ten national monuments and parks listed, she will have to settle for seeing just two of them. In how many ways could the two sites chosen include sites in only one state? New Mexico Arizona California Gila Cliff Dwellings Canyon de Chelly Devils…

24 Find the total number of times I go picking during the week and month. Also, find the square root of 60, D210, and 55. How many possible outfits can I create with 5 pairs of shoes, 4 shirts, and 2 pairs of jeans?

Ara iS trying to pick her college classes. She must pick between 3 writing classes, 2 math classes, 4 science courses and 3 electives. She must choose exactly one class from each subject How many course loads can Ara select? Select one: 27 36 12 72

10 The 4th term of the expansion (2x-3y)"

How many outfits are possible #ith pairs of jeans 8 t-shirts; and pair of shoes? 189 168 135 105

Directions: Read and understand each question carefully. Write the letter of the correct answer on your answer sheet. In how many ways can you arrange 7 books on a shelf? A. 360 B. 72,050 C. 5,040 D. PARALLEL

252 1+4 + (1+9)" are expansion of 02 terns in the 1) The first three and n Find the value of a

Text: Directions: Determine whether each scenario involves permutation or combination. Write the word PERMUTATION if it involves permutation; otherwise, write COMBINATION. Write your answers on a separate sheet of paper. Team of 8 basketball players needs to choose a captain and 3…

The number of rat a time is combinations of n objects taken 8 @ @or) (@-r) 3 Evaluate: 063) 8

Which of the following scenarios represents a combination? The arrangement of contestants in a beauty pageant The letters S, t, V, W are used t0 form 5-letter password for a security system The number of ways your family can be seated around the table, if your mother and father must sit next t0…

In how many ways can you arrange all the numerals 1 through 7? 720, 8, 49, 28, 5040.

9. Evaluate: C (7,4) A. 5 B. 15 C.25 D. 35 10. The first ten letters of the English alphabet are to be used by a certain company &s employee codes in sets of five . Find the number of combinations_ A. 25 B. 225 C. 252 D. 552

2. In how many ways can people be seated around a circular table? n-4, P= (4-1)! 31 (31(21(1) 6 waye

How many quadrilaterals can be formed from 10 points?

360 B. 720 1440 D. 5040 2. How many 7-letter words can we make with the letters in the word 'MATHEMATICS'? A. 7,920 B. 15,840 C. 31,680 D. 63,360 3. At the grocery section, Kyvhan wanted to select 2 diapers, 2 milks, 3 shampoos.

How many different license plates are possible if Kentucky uses three letters followed by four digits?

Attempt all the questions. Rewrite with absolute value |x| < 3 formed from the integers: 0, 1, 2, 3. How many different digit numbers can be 4, 5, or 2?

5. HOW MANY TWO DIFFERENT DIGITS CAN BE FORMED BY CHOOSING FROM 1, 2, 3, AND 4? A. 16 B. 12 C. 10 D. 7

Solve for n. P(n,2) P(n,3) = 720 P(n,n) = 5040 P(n,6) = 1 * P(n,5) 30 * P(5,4) = 80 * 6

A bag contains balls of five different colours Two are red; three are blue, ten are white, four are green and three are black. Balls are taken from the bag without looking; and not returned . What is the smallest number of balls that should be taken from the bag to be sure that two balls of the…

5. Using the digits 0, 1, 2, 3, 5, 7, 8, how many three-digit numbers can be formed if repetitions are not permitted? A 120 B 216 C 240 D 180

4 1o 31+4 6 4-(5I+ 31)

5. Using the digits 0, 1, 2, 3, 5, 7, 8, how many three-digit numbera can be formed if repetitions are not permitted? A 120 B. 216 C.240 D. 180 6. There are 4 trails that lead to a scout camp on a hill, In how many ways can a scout go to the camp and go down by going up one trail and down by a…

Use Pascal's Triangle to expand (x + 2)5

I took a 10-item Mathematics problem-solving test; now many guys can you lead! Problems solve? 252 B 254 256 D_258 how many ways can a committee of 5 be formed from juniors and seniors? (The committee must have seniors) 350 B. 355 360 386

What is the distinguishable permutation of the letters of the word EVEN?

The class consists of 10 boys and 15 girls. 4 How many such options for student selection Are there 3 boys and 1 girl in each version?

14. Which is true about the two situations? 1 Selecting the fruits in making fruit salad. I The password of the safe box is 736. Uv" < 1 ~sao 25 (^ 6,1 < e6 <O 0 , AS Both situations are permutations because order is important. B. Both situations are combinations because order is not important.…

16 VOJu3d How many different words can be formed with the letters of the word 'FACTORIAL' such that the vowels always come together?

A 3-letter code is created using the letters from the word COLUMBIA. How many different 3-letter codes can be created? 40,320 120 6,720 336 56

Evaluate (show all your work): 6.) 61 9.) 5! 21 7.) 91 10.) 10! 81 8.) 101

A. Find the number of permutation of letters of each word. 1. BASKETBALL 2. DIFFERENT 3. STATISTICS 4. ACCEPTANCE 5. LEARNING

Solve the following problem: Can you list all possible arrangements of the letters RED?

6. 8C3 + 6C1 7. 8C2 - 8C6 8, 11C4 3C3 9. 12C8 / 5C4 10. 7C2 x 6C3

2) Find the middle term(s) in the given expansions! a b)

16. In how many ways can a committee of 7 students be chosen from 9 juniors and 9 seniors if there must be 4 seniors in the committee? A. 10,584 B. 1,764 C. 210 D. 84 Jane wants to solve a system.

A seven-character insurance account number must be five letters of the alphabet followed by a two-digit number. How many different addresses of this kind are possible? Both letters and numbers are without repetition.

How many ways are Inara Vonckag Ieha arrangements out of the word DISCOVERY?

Use the binomial theorem to expand the polynomial (2x 3y)4 . Upload an image of your answer when you are finished:

Problem 1: In how many ways can in & row? we arange different fruits if we want t0 arrange it 2 Keyword: Permutation Combination Answer: Type of Permutation or Combination Answer: Substitute: Value of Formula: Simplify and Solve: Conclusion:

How many two digit numbers can YoU make using the digit cards? 7 0 2

bukjecl aie KEpl [Uyeltiei" "In how many ways can 6 students be seated in a row of 6 seats if 2 of the students insist on sitting beside each other?" "Suppose you are the owner of a sari-sari store and you want to put 12 pieces of canned goods in a row on the shelf. If there are 3…

B Problem solving Read and analyze the following situations then, answer the questions that follows. A certain password consists of 3 different letters of the alphabet where each letter I5 used only once. How many different possible passwords are there?

How many 3-digit numbers can be formed (only using the digits 0-9) if all the numbers formed are less than 700?

Find the coefficient of 139y^2 in the expansion of (x + 2y)^15. The coefficient of 239y^12 is 7557296947200.

9. How many ways can you arrange the 5 chairs in a row? a. 120 b. 72 c. 50 d. 210

8) How many ways can JANE, LORNA, JAM, IAN, and TRISH be seated around a table such that Jam and Ian never sit together? 12 C. 24 9) @raacbuffet, there are 10 different appetizers from which to choose. The appetizers are arranged on a revolving tray. 345,220 How many ways…

How can a baseball team manager align nine players in the lineup? 362,880 23,800 d. 1,818 Consider the word PEPPERS. How many unique arrangements can be made with these letters? 218 420 520 230 How many ways can yellow, red, and green balls be arranged in a row? 18,224 23,550 26,920 27,720 10.…

Find the number of different arrangements of the set of the following six letters: 0, 2, k, c, +, ?. A circle has 10 randomly placed points. In how many ways can you form each polygon listed below? Triangle, Rectangle.

What formula is used to determine the number of arrangements of objects in a circle? C.(n-1)! D (n-1)! #Ps= 6720, what is the value of n? 70 8 A family is being arranged in a line for a group.

LEARNERS ACTIVITY: Solving Problems involving Permutations and Combinations ACTIVITY Directions: Answer the following: The first number is done for you. Express the following product in simplest factorial form: 9!10 Answer: 10!15 [4!3 - 1!8] / [7!5!4!3!2!] Express the following factorial…

26. If n is a positive integer, show that âˆš(n^2 + 4n) can be expressed as (n + 2) using the Binomial Theorem.

Match Column A with the correct expression in Column B. How many committees with five accountants and three lawyers can be formed from a selection of six accountants and eight lawyers? Determine the number of different permutations of two of the five vowels a, e, i, and u. C(6,2) P(5,2) Find…

How many ways can the letters of the word "MATHEMATICS" be arranged? Keep Trying: How many three-digit even numbers can be formed with the digits 2, 4, and 8?

Three-digit numbers divisible by 3 are to be formed using any of the digits 0, 1, 3, 5, and 9. How many of this kind can be formed such that digits cannot be repeated?

Determine whether each of the followng is True or False 1.) 10! 10 x 9 x 8! TRUE FALSE 2.) 6! x 31 18! TRUE FALSE

9. Find the unknown in P(7,4) = B. 840 B. 1680 C. 10,080 D. 40,320

Pick 3 items from 10 in any order, where n = 10, r = 3. The total number of ways of making the selection are

1. C(7,5) = 21 2. C(6, r) = 20 3. C(10, 4) = 210 4. C(n, 3) = 35 5. C(r, 2) = 28

10. C (14, 10) =

12. Seven Grade 10 students, boys and girls, decided to have their group study at Mathematics Park. Only boys must sit beside each other. What is the possible arrangement of them around a circular table? Which of the following is the possible arrangement of 8 beads in a bracelet? …

Which of the following situations illustrates combination? Arranging books on a shelf. Assigning telephone numbers at home. Choosing household chores to do after class. Selecting posters to hang on the walls of your room.

In how many ways can 11 different books be arranged on a shelf? * 39,961,800 39,916,080 39,691,800 39,916,800

The number of permutations of n things taken at a time is equal to nPr.

A circle: How many quadrilaterals can be formed using any 4 of the seven points marked on the circle? Options: A. 20 B. 35 C. 70 D. 15

16, In How many ways can people arrange themselves in row for picture taking? 17, In how many ways can bicycles be parked If there are avallable parking spaces?

Text: General Direction: Read each item carefully. Write the letter of the best answer on the space provided. Explain your answer for each item by showing your solutions. Use an extra sheet of paper for the solutions. Quarter 3 Week 1: ILLUSTRATING PERMUTATION SCORE: The possible race results…

Letters digits. How many licenses a license #ok must have. Three are possible.

25*. How many even 3-digit positive integers can be written using the digits 1, 2, 4, 7, and 8?

if P(7, x) = 7!/3!, what is x? A. 8 B. 6 C. 4 D. 2

7. How many different ways can the letters of the word BANANA be arranged? A. 5 B. 6 C. 50 D. 60 In a family of 7, how many arrangements can be done during a circular family dinner? A. 207 B. 720 C. 5,004 D. 5,040 11. In how many ways…

Let N be the number of elimination games. 1010*9*8*7*6x514232212 = 101N - C(10, J)21(10-7)1 2421

9. C (n, 4) = 10. C (11, r) =

C(n,r) = 20 points (n-r)lr! Find the value of the following, (Show your solution. 2 pts each) C(7,2) C(5,4) C(24, 20) * C(10, 6) C(8,21) * C(7,51)

A committee of 3 people is to be chosen from 5 women and 7 men. Find the number of different committees that can be chosen if there are more women than men.

Find the number of three-digit numbers that can be written using the digits (4, 2, 3) without repetition of digits.

A bookshelf has n diffcrent Algebra books and thrce different Geomet books_ If there are 5 040 ways to arrange the books on the shelf; many Algebra books are on the bookshelf? B. 5 D. 7 Use this situation for items 10 12 Find the number of differ arrangements of the set of the seven letters…

If you are playing SCRABBLE and there are 7 distinct letters on your wooden tiles, how many "words" can you form using all these letters? * 6,720 5,040 5,207 6,040

There are three dials on a combination lock. Each dial can be set to one of the numbers 1, 2, 3, 4, 5 The three digit number 514 is one way the dials can be set as shown in the diagram. a) Work out the number of different three digit numbers that can be set for the combination lock. (2) b) How…

Match the correct value 10 points 24 121 120 41

There are 8 books on a shelf. In how many ways can you select 4 books. A) 10 C) 50 B) 30 D) 70.

For these, if each signal uses 3 flags? In how many ways can 5 bicycles be parked if there are available parking spaces? Elc and different music books.

Test V. EVALUATING: Evaluate the following permutations. Write your answers on a separate sheet of 'pad paper. 4P2, 4P3, 4C3.

12. If we have a total of elements, the integer (1_ 7). Now, how many unique sequences of three elements (2, 5, 7) exist from this set? In the given problem, which of the following formulas should be used in solving the problem? A. nPr B. nCr C. nCr D. nPk

In how many ways can 6 keys be arranged in a key ring? 15 30 45 60

Em found out that she has 10 bills in her wallet, 4 are one thousand-peso bills, 3 are five hundred-peso bills and 3 are one hundred-peso bills. How many permutations are there?

Ten people posing for a picture. No three points are collinear. Creating triangles from a drawn 5-sided polygon. Diagonals that can be found. Determining the total number of different ways to arrange the top three awardees. Placing books on a shelf. Cards formed from a standard deck of 52…

Answer the following problems considering that repetition is allowed in the space provided before each number. The first situation is: A young lady decided to choose 2 flavors from 5 of her favorite flavors of ice cream to be served on her 5th birthday. How many combinations are…

Find the number of distinguishable permutations of the word EDUCATED. a. 1,680 b. 1,080 c. 20,160 d. 40,320 Peter Pan has pairs of shoes, pairs of pants, and 14 t-shirts. How many possibilities can he have?

2. Calculate P(11,4) A. 55440 B. 7920 C. 2520 D. 990

Application: Try to work on this. Give the combination of each of the following, given the number of objects (n) and the number of objects taken at a time (r). The first number is done for you: number of objects (n) = 5, number of objects taken at a time (r) = 3. c(n,r) = n! / (r!(n-r)!) …

7. In how many ways can 5 boys and 5 girls be arranged in a row for picture taking if: a) all boys are together? b) boys and girls are arranged alternately?

III: Assessment Application/Outputs Directions Choose the letter of the correct answer. It is a selection of objects from a set. A. combination B. differentiation C. permutation D. distinction Which of the following situations illustrates a combination? arranging books on a shelf drawing…

How many different ways can the 8 persons be seated in a circular table? A. 5,040 B. 5,220 C. 5,440 D. 5,520

P (8, 3) =

How many chords can be formed from the circumference of the circle? If there are even points formed on the circumference. How many different 10-member committees can be formed from the senators of the country?

Write P if the situation/problem is involving permutation and N if Not Write the corresponding notation if the problem involves permutation. 1 , Ten runners join a race: In how many possible ways can they be arranged a8 sklirst, second, and third placers?

From a class with 40 students, 8 students will be chosen to join the science field trip. In how many ways can the students be chosen? Given: n- Formula: C(n,r) = n! / (r!(n-r)!) Solution:

6. In how many ways can the letters of the word ""CLASSICAL"" be arranged? a. 362,880 b. 22,680 c. 360 d. 72

Find the value of P(5,4)+ C(5,1) B. 5 C. 6 D. 125

And YELLOW, where three marbles have to be kept one upon another, a game has to be made from marbles of three colors: RED, GREEN, and another. In how many ways can these marbles be arranged? Select one.

DIRECTION: Provide the answer to the following given situation. Justify the outcome of your solution: In the player's jersey, there are 2-digit numbers. How many different numbers can we get? Choose.

Find the number of different ways that an instructor can choose 3 students from a class of 17 students for a field trip.

In how many ways can all the letters of the word "MONTREAL" be arranged if the letters R, E, A, and L must appear in order as the word REAL in all arrangements?

In how many ways can the letters of the word SWIFTNESS be arranged if all the letters are used and the vowels are kept together?

A combination lock like the one shown has three dials. Each of the dials has numbers ranging from 1 to 8 How many different combinations are possible with the lock? 343 combinations 48 combinations 512 combinations 24 combinations

From a group of 12 student representatives, 6 will be chosen to work on a committee: How many committees of 6 are possible if Sally & Sam must be on the committee?

Question 2 To choose the three players fairly; Coach Bennet decides t0 ser up a free throw contest The three players who make the most consecutive free throws will get to g0 to the summer basketball clinic: Part A Question How many different orders of top-three finishers are possible? Drag the…

Determine whether the situation represents a permutation or combination; then solve How many ways can a president; vice president; and treasurer be elected from a group of 20 students? Sample Answer: 1,234 59,280 6,840 1,140 1,150 None of the Above

There are 20 horses in the Kentucky Derby. How many different ways can the horses finish 1st, 2nd and 3rd place? 60 6,840 1,140 20

How many odd four-digit numbers can be formed from the digits 1, 17. 2 3 and 42 Write the possible odd numbers.

What is nif -448x^3 appears in the expansion of (x + 2y)^3.

From 4 red, 5 green, and 6 black ballpoint pens, how many selections of 9 ballpoint pens are possible if 3 of each color are to be selected? Clue: 1st activity n=4, r=3; 2nd activity n=5, r=3; 3rd activity n=6, r=3.

How many different paths will spell the word CASH using the diagram below?

Find the number of possibilities using permutations or combinations The student body of 10 students wants to elect a president vice president secretary,_ and treasurer:

When we randomly select a permutation of {1,2}, what is the probability that 1 immediately precedes 2? Given that n = 8, what is the probability? Write your answers in decimal form and round off to the nearest hundredths.

2 . How many different 3-digit numbers can be formed from 0, 1, 4, 6, and 8 if no repetition is allowed? b. repetition is allowed? repetition is allowed but all numbers formed are odd? repetition is allowed but all numbers formed are even? 240

25. How many different arrangements of letters can you make from the word "TENNESSEE"? 362 880 3 780 181 440 90 720

Choosing books from a set of books is an example of combination, differentiation, integration. When evaluated, what is the value of C(6)? 48 permutation.

Title: "Permutations and the Fundamental Principle of Counting" Fundamental Principle of Counting (FPCI) states that an activity can be done in n ways; if one activity can be done in n1 ways and another activity can be done in n2 ways, then the activities can be done simultaneously in n1 * n2…

Find the number of permutations of the letters in the word BOOK. a. P = 4! / (4-2)! = 12 b. P = 4! / 2! = 12 c. P (4-2) ! = 2! = 2 d. = 4! / 2!1!1! = 2

Evaluate: 4. 12! A. 479,100,600 B. 479,101,600 C. 479,110,600 D. 479,001,600

What is the coefficient of x^7 in the expansion of (x + y)^12?

2. Six actors and eight actresses are available for a play that requires 4 males and 3 females. How many different cast lists are there? A. 120, 960 B. 40, 320 C. 20, 160 D. 576

q ~o number of arrangements in a row of 7 objects taken 2 at a time Er ` . | 1 [ 'P '1 . ' , . ( ( JE + uax81 swalqo 0T JO MOI â‚¬ UJ SJUJU3BuEIJe JO Iaqunu a time 6 7 ZI ~o fOL J8 9 uaxe} 81231q0 8 jo

Match each expression in column to its corresponding expression in column 2 nPz 3.nPn nPo 5.nl 6. nPs b. n(n-1)(n-2) / (2)(1) 3n! d:n n^n _ n t.nl

For number 3-4: In how many ways can a group of 7 persons arrange themselves? Your answer 3. In a row of 7 seats? 2 points 40,320 5,040 720 120 Around a circular table? 2 points 40,320 5,040 720 120

3. Five Ladies apply for 3 saleslady positions. In how many ways can These position be filled by the lady applicant

The manager at Dunder Mifflin needs to send off their 6 salespeople and 5 warehouse workers on a sales call. How many combinations of salespeople and warehouse workers are there? Review Pascal's triangle here: 462 150 Click Submit to complete this assessment. Question 6 of 6 Save and Submit

Which of the following is the permutation of 10 objects taken 2 at a time?

How many permutations can be made from the letters of the word VACCINATION? 2,494,800 79,833,600 453,600 55,440

The number of ways to arrange 5 people in a row out of a class of 8 people is

FC6 Ibub 1 V8 Ebp? Boo? Sgcb-28 Jbcb _ 8o8 Pa Sbe? 1) RCI- gcI gU I ZC IbcL 5bA fb4R goo? Sgcr :Jb Rgo8 21 Xopk gcL:8 1 8C4.3c2 ~bCb @ * goo 8 24}l Roo gc5 . RCL 806 Tcb JbCb I6ZX Vb Roo? RoR gckel 80 =8} P What does "C" in 8C6 for no: 1 mean and how come it is equal to 28? dont get it. Can…

If a group of 5 people participate in a pie eating contest, how many ways can 1st, 2nd, and 3rd place be awarded? * 6 ways 30 ways 12 ways 60 ways 720 ways None of the above.

4. In how many ways can five people sit at a round table if three of them insist on sitting next to each other?

In how many ways can 12 members of a varsity volleyball team be chosen from 30 persons who tried out? 86 480 325 86 493 225 86 590 445 86 370 665

70 Il "'0+8 iiu Jo anjBA aq1 SI JEYA `Sâ‚¬ = ') JI

In how many ways can 9 runners finish a race in first, second, or third place?

In how many ways can 8 women be arranged in a straight line? 40, 320 10, 260 5, 040 24, 240

Consider the set of numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). How many digit codes can be formed? The code may not contain repeated characters. If the code may not contain repeated digits, different codes can be formed.

How many selections can be made if a committee of 9 people is to be formed from a population of 16 people, but Kiana, Sham, and Yanika must be on the committee?

Copy and solve in a short bond paper A_ Evaluate the following P(8,5) 1. 312! 2. P(4,4) 3. P(6,3)

Determine the number of possible sample of the following if the sample size is n = 3 use the combination formula: N = 20 O a. 140 O b. 2140 O c. 1140 O d. 111400

To win the trifecta you must pick the first, second and third place winners for Ihe race_ If 10 horses are racing; how many different outcomes are there for the trifecta? 720 3,628,800 120 1000 none of the above

2. Find the number of permutations for arranging the letters S, C, I, E, N, C, E in a row.

16. You are setting the combination in a four-digit lock: You want to use the numbers 1 2 3 4 but don't care what order they are in. Permutation, 24 Combination; 24 C. Permutation; Combination, 1

A Math varsity coach is selecting two members to compete in an upcoming Math competition through elimination: The top scorer will be the Primary Competitor and the second top scorer will be the Secondary Competitor. Five members - Thea, LJ, Anthony, Joyce, and Xander - are vying for the spots.…

Which of the following statements is true? a. Arrangement is important in permutation. b. In combination, arrangement is not important. c. Combination is permutation divided by r. d. Information is incomplete. e. iii only except iv. f. iv.

3. In how many ways can the letters in the word "Missouri" be arranged?

Permutation Combination #diger Evolcnnu oui Fdulon Ten Grade 10 students are chosen from eighteen to be members of the Grade 10 Assembly.

How many different signals can be made by arranging 9 banners in a line if 4 banners are red, 3 are white and the rest are blue?

Plates of private cars have 3 letters followed by 4 numbers if letter and number cannot be repeated; how many can be made?

In how many ways can you arrange 6 Mathematics books, 3 Science books, and 4 English books on a shelf such that books of the same subject are kept together? In a panel of 4 members, they will be selected from S men and $ women. In how many ways can 2 of the panelists be men and the other two be…

How many six-digit numbers can be formed from the digits 1, 2, 3, 5, and 6 if repetitions are allowed? A. 702 B. 720 C. 46,656 D. 46,665

Use the formula for nCr to evaluate the given expression: 15C12 * 7C6. 15C12 = 15! / (12! * (15-12)!) = 15! / (12! * 3!) = (15 * 14 * 13) / (3 * 2 * 1) = 455. 7C6 = 7! / (6! * (7-6)!) = 7! / (6! * 1!) = 7. Therefore, the expression evaluates to 455 * 7 = 3185.

How many ways can you arrange a blue ball, a red ball a black and a yellow ball in a row? 100 120 24 60

There are 6 ways that persons can be seated at a round table. This example of Non-permutation Permutation 9/ deleting a single B. Circular permutation Permutation of non-distinct Objects

Activity 2: FACTORIAL NOTATION Evaluate each of the following examples: 7! = 7.6.5.4.3.2.1 = 5,040 10! = 10.9.8.7.6.5.4.3.2.1 = 3,628,800 Remember: n! = n(n-1)(n-2)...(3)(2)(1), where n is a positive integer; 0! = 1 n! is read as "n factorial" 2^4 = 2.2.2.2 = 16 3(11 - 8)! = 3.3.2.1 = 18 5^2 =…

Column A permutation with repeated elements G-t (n- nl nInz!na nl nPr circular permutation circular permutation taken a few at a time D. permutation of objects taken a few at a time E. permutation of objects taken all at a time

II: How many different ways can the letters of each word be arranged? Show your solution. (15 points) 1_ PROBABILITY 2. MISSISSIPPI 3. REARRANGE

4. Evaluate: P(7, 5) A. 21 B. 35 C. 250 D. 2520

A close friend invited Czairyn to her birthday party. Czairyn has 4 new blouses (stripes, with ruffles, long-sleeved, and sleeveless) and 3 skirts (red, pink, and black) in her closet reserved for such occasions. Assuming that any skirt can be paired with any blouse, in how many ways can…

From a group of four men and seven women, six are arranged in a row. How many different arrangements are there with each of the following properties? 1. The first three people in the row are men, and the second three are women. 2. Men and women alternate, with the first person in the row being…

How many five-digit numbers with different digits are there if the first and second digits are even?

There are 10 members of a club. How many different 3 member committees can you have?

Use Pascal's triangle to expand (a + 2b). Show work. (TA CI) Row 0: 1 Row 1: 1 1 Row 2: 1 2 1 Row 3: 1 3 3 1 Row 4: 1 4 6 4 1

3. How many distinct permutations can be made from the letters of the word " INDEPENDENCE"? n=12, N=3, D=2, E=4

Iow many ways can 6 boys and 6 girls be seated at & round table if: particular girls must sit together

3. How many 5-letter permutations can be formed from the letters in the word ANCHOVIES? a. 1680 b. 3 024 c. 6720 d. 15 120

Write down the general term in the binomial expansion of (3x).

Use the Binomial expansion of (1 + 2x)20 to evaluate 1.000224, correct t0 /2 decima places

At a used car lot; 9 different car models are to be parked close to the street for easy viewing; but there is only space for 5 cars. How many ways can 5 of the 9 cars be parked in a row? Show your work t receive full marks.

A, ^, 7, and Hi is 90ring one file letter. May 0 of ways face could row find the total number 2w a do miss.

ABSOLUTELY RIGHT A. Direction: Use Pascal's triangle to find the expansion of the following binomials. (2 points each) 1. (x + y)^2 Given: n = 2 Expanded form: x^2 + 2xy + y^2 2. (x - y)^2 Given: n = 2 Expanded form: x^2 - 2xy + y^2 3. (x - 3y)^2 Given: n = 2 Expanded form: x^2 - 6xy +…

Beginning? Make an organized list. 2. A baseball team won two out of their last four games. In how many different orders could they have two wins and two losses in four games? Make a table and look for a pattern.

2 How many permutations of the letters in the word CANADA do not begin with an A?

Use the binomial theorem to find the values of the following: VI,001 correct to six decimal places. [2 Marks]

Decide numbers can be formed if each number starts with 27 and no digit 25. How many 6-digit numbers appear more than once? c 213 127 200 680 70 b 296 010 determined by & points, no three of which are collinear?

Grace is making a movie and needs to cast some actors. There are 3 actors interested in playing the female lead role, and 6 actors interested in playing the male lead role How many different ways can Grace cast the film?

Question 5 I1 Points Out of fifty runners in a race, we want to know how many ways different runners can come in first, second, third, and fourth place. Calculate the number of ways that fifty runners can finish in first, second, third, and fourth places. Fill in the blanks below with the…

A four-letter code is to be formed using four of these cards: (a) Find the number of different four-letter codes that can be formed. (b) Find the number of different four-letter codes which end with a consonant.

Four different colored flags can be hung make coded signal How Many signals if & signal consists of the display of one more flags? be made

A basketball coach will choose 5 players from a group of 8 players to start the next game. How many different groups of starting players are possible?

How many 5-digit numbers can be created using the digits 2, 3, 5, 7, and 8 without repeating any digits within that 5-digit number?

23.) How many 3 digit even number can be formed from set {1,2,3,4,5} without repetition? 10 24 50 60

Alexander is designing a new board game and is trying to figure out all the possible outcomes. How many different possible outcomes are there if he flips a coin and rolls a fair die in the shape of a cube that has six sides labeled 1 to 6?

Find the number of ways for 4-digit even numbers greater than 4000 to be formed by using digits 2, 3, 4, 5, 6, and without repetition.

Find the following terms of the Fibonacci sequence by using the Binet's formula: Show your solution/process to get the answer; 5 points each. Item No solution, no points. 50th term 70th term

Show that âˆš(nCr) = âˆš(n! / (r! * (n-r)!)) Note: nCr represents the combination of n items taken r at a time. r!(n-r)! represents the product of r factorial and (n-r) factorial.

The diagram shows five cards with letters as shown: 4) Diagram: Find the total number of ways of arranging all cards in a row. 6) Find the number of arrangements such that letter E and A must be adjacent to each other:

17"Cr "D-"+ 'D1-" that Show

How many distinct permutations can be formed from all the letters of the word sociological?

In a classroom, there are 23 girls and 25 boys. The class is to elect a President, Vice President, and 2 Treasurers. What is the probability that if students were elected at random, all three positions were filled by girls? 2C2: 2P3 / 25C2: 25P3

Activity I: LET'S SOLVE THIS! Find the number of three-digit numbers that can be written using the digits from the set {1, 3, 5}, assuming repeated digits are not allowed. Answer: 6 (135, 153, 315, 351, 513, 531) A box contains 3 balls: red, white, and blue, respectively. If they are identical…

In how many different ways can 7 potted plants be arranged in a row? 720 210 5 040 2 520

Direction: Fill in the blanks with the correct letters/KuSwec A. You have to create your 4-pin code on your cellphone, you can use the letters M-A-T-H. Continue the pattern for your pin code: MATH, MAHT, MTHA, MTAH, MHAT, MHTA, ATHM, THMA, HMAT.

Find the coefficient of the t4 term in the expansion of (4t S 3)5

Use Binomial Theorem to show that (6 + 14) is divisible by 10.

The number of different orders of yerticu taken at a the actual number combination? Run 1 P(4,31). What

Although Megan is interested in seeing the ten national monuments and parks listed, she will have to settle for seeing just two of them. In how many ways could the two sites chosen include sites in only one state? New Mexico Arizona California Gila Cliff Dwellings Canyon de Chelly Devils…

24 Find the total number of times I go picking during the week and month. Also, find the square root of 60, D210, and 55. How many possible outfits can I create with 5 pairs of shoes, 4 shirts, and 2 pairs of jeans?

Ara iS trying to pick her college classes. She must pick between 3 writing classes, 2 math classes, 4 science courses and 3 electives. She must choose exactly one class from each subject How many course loads can Ara select? Select one: 27 36 12 72

10 The 4th term of the expansion (2x-3y)"

How many outfits are possible #ith pairs of jeans 8 t-shirts; and pair of shoes? 189 168 135 105

Directions: Read and understand each question carefully. Write the letter of the correct answer on your answer sheet. In how many ways can you arrange 7 books on a shelf? A. 360 B. 72,050 C. 5,040 D. PARALLEL

252 1+4 + (1+9)" are expansion of 02 terns in the 1) The first three and n Find the value of a

Text: Directions: Determine whether each scenario involves permutation or combination. Write the word PERMUTATION if it involves permutation; otherwise, write COMBINATION. Write your answers on a separate sheet of paper. Team of 8 basketball players needs to choose a captain and 3…

The number of rat a time is combinations of n objects taken 8 @ @or) (@-r) 3 Evaluate: 063) 8

Which of the following scenarios represents a combination? The arrangement of contestants in a beauty pageant The letters S, t, V, W are used t0 form 5-letter password for a security system The number of ways your family can be seated around the table, if your mother and father must sit next t0…

In how many ways can you arrange all the numerals 1 through 7? 720, 8, 49, 28, 5040.

1 2 3 4 5 ... 29