Quiz about Counting Methods (Permutation and Combination)

Question 1

A team of 8 basketball players needs to choose a captain and co-captain.

Accepted Answer

56

Answer

64

Answer

15

Answer

40,320

Question 2

A group of 25 people are going to run a race. The top 8 finishers advance to the finals.

Accepted Answer

1,081,575

Answer

200

Answer

4.3609 x 10¹⁰

Answer

0

Question 3

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?

Accepted Answer

64

Answer

14

Answer

24,024

Answer

2184

Question 4

A group of 45 people are going to run a race. The top three runners earn gold, silver, and bronze medals.

Accepted Answer

85,140

Answer

135

Answer

14,190

Answer

91,125

Question 5

5 out of 13 students will ride in a car instead of a van

Accepted Answer

1,287

Answer

154,440

Answer

371,293

Answer

65

Question 6

There are 45 applicants for three Computer Programmer positions.

Accepted Answer

14,190

Answer

135

Answer

85,140

Answer

91,125

Question 7

A lock has four dials. On each dial are the digits 0 to 9. How many possible combinations are there?

Accepted Answer

10,000

Answer

40

Answer

5040

Answer

6561

Question 8

A lock has four dials. On each dial are the digits 0 to 9. How many possible combinations are there if you cannot reuse a number?

Accepted Answer

5040

Answer

40

Answer

6561

Answer

10,000

Question 9

When does the order in which you are choose matter?

Accepted Answer

Permutation

Answer

Combination

Question 10

When does the order in which you are choose not matter?

Accepted Answer

Combiniation

Answer

Permutation

Question 11

What is the r value for choosing 5 cards from a standard deck of cards?

Accepted Answer

5

Answer

2

Answer

13

Answer

52

Question 12

How many ways can 8 cheerleaders be chosen for 3 positions on the cheer team?

Accepted Answer

56

Answer

24

Answer

128

Answer

336

Question 13

How many ways can 9 runners medal (Gold, Silver or Bronze) in a race?

Accepted Answer

504

Answer

27

Answer

84

Answer

216

Question 14

Jim draws 4 cards from a deck of cards.  What is the probability of all 4 cards being clubs?

Accepted Answer

13C4 52C4

Answer

13C4 52P4

Answer

1 52C4

Answer

1 52P4

Question 15

James purchased 3 shirts, 3 jackets and 2 pairs of pants.  How many different outfits using a shirt, a jacket, and pants are possible?

Accepted Answer

18

Answer

8

Answer

54

Question 16

The value of 5! is ____.

Accepted Answer

120

Answer

25

Answer

15

Answer

720

Question 17

Which of the following would you use to calculate the number of ways to elect a President, a Vice President, and a Secretary from a group of 12 individuals. Think: Does order matter?

Accepted Answer

Permutation

Answer

Combination

Answer

Neither

Question 18

What does ₁₀C₅mean?

Accepted Answer

Combinations with 10 choices and 5 positions

Answer

Combinations with 5 choices and 10 positions

Answer

Permutations with 5 numbers and 10 operations

Answer

Permutations with 5 hot dogs and 10 drinks

Question 19

What is the value of ₅P₂?

Accepted Answer

20

Answer

60

Answer

10

Answer

15

Question 20

How many 2-digit numbers can you make using the digits 1, 2, 3, & 4 without repeating the digits? Think: Does order matter?

Accepted Answer

12

Answer

90

Answer

100

Answer

24

Question 21

Which of the following would be used to calculate the number of ways one could choose 3 toppings for a sundae out of a list of 15?

Accepted Answer

Combination

Answer

Permutation

Answer

Neither

Question 22

A team of 17 volleyball players needs to choose three players to refill the water cooler. How many different ways can the players be chosen?

Accepted Answer

680

Answer

3360

Answer

560

Answer

4080

Question 23

Ambry must submit 4 paintings as part of her application to art school. If she has 25 to choose from, how many ways can she pick 4? Think: Does order matter?

Accepted Answer

12,650

Answer

303,600

Answer

100

Answer

254

Question 24

At  a New Car Dealership a particular model comes in 4 trim levels, 5 different colors, and 3 different interiors. How many different versions of this car model can be created from these options?

Accepted Answer

60

Answer

180

Answer

23

Answer

12

Question 25

How many ways can you arrange 10 books on a shelf?

Accepted Answer

3,628,800

Answer

10

Answer

100

Answer

50

Question 26

How many different arrangements can be made from WATER?

Accepted Answer

120

Answer

5

Answer

10

Answer

0

Question 27

How many different arrangements can be made from MATH?

Accepted Answer

24

Answer

10

Answer

0

Answer

6

Question 28

How many different arrangements can be made from COLLEGE?

Accepted Answer

5040

Answer

28

Answer

720

Answer

35280

Question 29

How many ways could you choose 2 different letters from PROBABILITY?

Accepted Answer

55

Answer

3,628,800

Answer

28

Answer

403,200

Question 30

Simply the expression: 9P4

Accepted Answer

3024

Answer

36

Answer

120

Answer

35

Question 31

A(n) ______ is a list of all possible outcomes that may occur.

Accepted Answer

sample space

Answer

event

Answer

outome

Answer

counting principle

Question 32

A single coin is flipped 7 times. How many different outcomes are possible?

Accepted Answer

128

Answer

14

Answer

49

Answer

823,543

Question 33

The fundamental counting principle states that if you wish to find the number of outcomes for a given situation, simply ___ the number of possible outcomes for each step of the event.

Accepted Answer

multiply

Answer

add

Answer

subtract

Answer

divide

Question 34

Suppose you are dealt three cards from a standard deck of 52 cards. How many different outcomes are possible for what your three cards might be?

Accepted Answer

132,600

Answer

140,608

Answer

124,800

Answer

156

Question 35

Noah's wallet contains a $1 bill, a $5 bill, and a $10 bill. If Madie takes two bills from his wallet (without replacing any), how many different outcomes are possible?

Accepted Answer

6

Answer

4

Answer

8

Answer

9

Question 36

How many 4 letter permutations can be formed from the letters in the name jayci?

Accepted Answer

120

Answer

64

Answer

24

Answer

32

Question 37

A ____ is a specific order or arrangement of a set of objects or items in which order DOES matter.

Accepted Answer

permutation

Answer

combination

Question 38

A ____ is a specific order or arrangement of a set of objects or items in which order does NOT matter.

Accepted Answer

combination

Answer

permutation

Question 39

In how many different ways can 3 raffle tickets be selected from 20 tickets if each of the 3 ticket holders wins a different prize?

Accepted Answer

6,840

Answer

402,460

Answer

32,064

Answer

12,300

Question 40

Suppose there are 8 girls and 11 boys in the Junior class. How many ways can 3 girls and 4 boys be selected for a volleyball team?

Accepted Answer

18,480

Answer

386

Answer

720

Answer

2,460

Question 41

Suppose there are 12 students in the Statistics class. Mrs. Colwell selects 4 students to go home early. In how many ways can she do this?

Accepted Answer

495

Answer

11,880

Answer

20,736

Answer

16,777,216

Question 42

In how many ways can the letters in the word 'Kane' be arranged?

Accepted Answer

24

Answer

8

Answer

16

Answer

32

Question 43

How many different seating arrangements are possible for our stats class of 10 students?

Accepted Answer

3,628,800

Answer

1,000,000,000

Answer

2,800,300

Answer

12,300,064

Question 44

Which of the following is NOT an organizational strategy used in statistical counting methods.

Accepted Answer

pictograms

Answer

sets/lists

Answer

tables/grids

Answer

tree diagrams

Question 45

The cafeteria decides to allow students some options at lunch. Students may choose either milk or juice, chicken, pork, or steak, and potatoes or rice. How many different lunch combinations exist is a student is to pick 1 drink, 1 meat, and 1 side item?

Accepted Answer

12

Answer

8

Answer

6

Answer

9

Question 46

Which of the following situations is represented by this tree diagram?

Accepted Answer

3 shirt options, 2 pants options, and 2 shoe options

Answer

3 shirt options, 6 pants options, and 12 shoe options

Answer

2 shirt options, 3 pants options, and 1 shoe option

Question 47

How many outfits are possible with 5 pairs of jeans, 8 t-shirts, and 2 pairs of shoes?

Accepted Answer

80

Answer

15

Answer

40

Answer

10

Question 48

At  a New Car Dealership a particular model comes in 4 trim levels, 5 different colors, and 3 different interiors. How many different versions of this car model can be created from these options?

Accepted Answer

60

Answer

180

Answer

23

Answer

12

Question 49

Which of the following is an example of combination?

Accepted Answer

Choose 4 students in a class committee

Answer

Form a passcode with 4 digits

Answer

Students line up in a queue to assembly

Answer

Choose the chairperson, secretary and treasurer in a club

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