wayground logo

Free Printable Worksheets

NEW

Font size

S
M
L
XL
Worksheets

Counting Methods (Permutation and Combination)

Total questions: 60

Worksheet time: 3hrs 31mins

Name
Class
Date
1.
A team of 8 basketball players needs to choose a captain and co-captain.
a)
64
b)
56
c)
15
d)
40,320
2.
A group of 25 people are going to run a race. The top 8 finishers advance to the finals.
a)
200
b)
4.3609 x 1010
c)
0
d)
1,081,575
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? 
a)
64
b)
14
c)
24,024
d)
2184
4.
You go to Best Buy to purchase a new television. You have the following choices: LCD or plasma; screen size 27”, 32”, 36”, 41”, 51”, or 63” and manufacturer Sony, Vizio or Phillips. How many different televisions does the store have to offer? 
a)
18
b)
990
c)
72
d)
36
5.
A group of 45 people are going to run a race. The top three runners earn gold, silver, and bronze medals.
a)
135
b)
85,140
c)
14,190
d)
91,125
6.
5 out of 13 students will ride in a car instead of a van
a)
1,287
b)
154,440
c)
371,293
d)
65
7.
There are 45 applicants for three Computer Programmer positions.
a)
135
b)
85,140
c)
14,190
d)
91,125
8.
A lock has four dials. On each dial are the digits 0 to 9. How many possible combinations are there?
a)
40
b)
5040
c)
6561
d)
10,000
9.
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?
a)
40
b)
5040
c)
6561
d)
10,000
10.
When does the order in which you are choose matter?
a)
Combination
b)
Permutation
11.
When does the order in which you are choose not matter?
a)
Combiniation
b)
Permutation
12.
What is the formula for Combinations?
a)
n!∕(n-r)! r!
b)
n!∕(n-r)!
c)
r!∕(r-n)! n!
d)
n!
13.
What is the formula for Permutations?
a)
n!
b)
n!∕(n-r)!
c)
n!∕(n-r)! r!
d)
r!∕(r-n)! n!
14.
What is the r value for choosing 5 cards from a standard deck of cards? 
a)
2
b)
5
c)
13
d)
52
15.
How many ways can 8 cheerleaders be chosen for 3 positions on the cheer team?
a)
24
b)
56
c)
128
d)
336
16.
How many ways can 9 runners medal (Gold, Silver or Bronze) in a race?
a)
27
b)
84
c)
216
d)
504
17.
Your chores are to clean your room and take out the trash
Event A is you clean your room
Event B is you take out the trash
(¬ indicates "not")
What does A∩¬B mean
a)
You don't clean your room and take out the trash.
b)
You clean your room or take out the trash
c)
You clean your room and take out the trash
d)
You clean your room but didn't take out the trash
18.
Your chores are to clean your room and take out the trash
Event A is you clean your room
Event B is you take out the trash
(¬ indicates "not")
What does A∪¬B
a)
You clean your room or don't take out the trash
b)
You don't clean your room or take out the trash
c)
You clean your room and take out the trash
d)
You clean your room or take out the trash
19.
Your chores are to clean your room and take out the trash
Event A is you clean your room
Event B is you take out the trash
(¬ indicates "not")
What does ¬(A∩B) mean?
a)
You don't do one of your chores
b)
You don't do either of your chores
c)
You clean your room but take out the trash
d)
You don't clean your room but take out the trash
20.
Your chores are to clean your room and take out the trash
Event A is you clean your room
Event B is you take out the trash
(¬ indicates "not")
What does ¬(A∪B)
a)
You don't do both of your chores
b)
You don't do at least one of your chores
c)
You don't clean your room but take out the trash
d)
You clean your room but don't take out the trash
21.
You flip a coin three times. What is the probability of three consecutive heads?
a)
½
b)
⅓
c)
⅙
d)
⅛
22.
Which answer describes conditional probability  
a)
A conclusion drawn  based on what one 
already knows and 
on that alone
b)
The probability of 
some event A,
 assuming event B
c)
The number of 
favorable outcomes 
divided by 
the total number of 
possible outcomes.
d)
The occurrence of some 
event A automatically
implies the non–occurrence of a 
second event B.
23.
Jim draws 4 cards from a deck of cards.  What is the probability of all 4 cards being clubs?
a)
13C4
52P4
b)
13C4
52C4
c)
1
52C4
d)
1
52P4
24.
Eight racers are running and Tom wants to know his probability to earn a medal (Gold, Silver or Bronze).
a)
⅓
b)
⅗
c)
⅜
d)
⅝
25.
James purchased 3 shirts, 3 jackets and 2 pairs of pants.  How many different outfits using a shirt, a jacket, and pants are possible?
a)
8
b)
18
c)
54
26.
The value of 5! is ____.
a)
25
b)
15
c)
120
d)
720
27.
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?
a)
Permutation
b)
Combination
c)
Neither
28.
What does 10C5 mean?
a)
Combinations with 5 choices and 10 positions
b)
Combinations with 10 choices and 5 positions
c)
Permutations with 5 numbers and 10 operations
d)
Permutations with 5 hot dogs and 10 drinks
29.
What is the value of 5P2?
a)
60
b)
10
c)
20
d)
15
30.
How many 2-digit numbers can you make using the digits 1, 2, 3, & 4 without repeating the digits? Think: Does order matter?
a)
90
b)
100
c)
12
d)
24
31.
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?
a)
Permutation
b)
Combination
c)
Neither
32.
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?  
a)
3360
b)
560
c)
4080
d)
680
33.
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?
a)
12,650
b)
303,600
c)
100
d)
254
34.
What is the formula for combinations?
a)
n!∕(n-r)! r!
b)
n!∕(n-r)!
c)
r!∕(r-n)! n!
d)
n!
35.
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?
a)
180
b)
23
c)
12
d)
60
36.

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

a)

10

b)

100

c)

50

d)

3,628,800

37.

How many different arrangements can be made from WATER?

a)

5

b)

120

c)

10

d)

0

38.

How many different arrangements can be made from MATH?

a)

10

b)

0

c)

6

d)

24

39.

How many different arrangements can be made from COLLEGE?

a)

28

b)

720

c)

5040

d)

35280

40.

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

a)

3,628,800

b)

28

c)

55

d)

403,200

41.

Simply the expression: 9P4

a)

36

b)

120

c)

35

d)

3024

42.

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

a)

sample space

b)

event

c)

outome

d)

counting principle

43.

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

a)

14

b)

128

c)

49

d)

823,543

44.

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.

a)

add

b)

subtract

c)

multiply

d)

divide

45.

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?

a)

132,600

b)

140,608

c)

124,800

d)

156

46.

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?

a)

6

b)

4

c)

8

d)

9

47.

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

a)

64

b)

24

c)

120

d)

32

48.

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

a)

permutation

b)

combination

49.

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

a)

permutation

b)

combination

50.

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?

a)

6,840

b)

402,460

c)

32,064

d)

12,300

51.

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?

a)

18,480

b)

386

c)

720

d)

2,460

52.

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?

a)

495

b)

11,880

c)

20,736

d)

16,777,216

53.

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

a)

8

b)

16

c)

24

d)

32

54.

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

a)

1,000,000,000

b)

2,800,300

c)

12,300,064

d)

3,628,800

55.

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

a)

sets/lists

b)

tables/grids

c)

tree diagrams

d)

pictograms

56.

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?

a)

8

b)

6

c)

9

d)

12

57.
Which of the following situations is represented by this tree diagram?
a)
3 shirt options, 6 pants options, and 12 shoe options
b)
3 shirt options, 2 pants options, and 2 shoe options
c)
2 shirt options, 3 pants options, and 1 shoe option
58.
How many outfits are possible with 5 pairs of jeans, 8 t-shirts, and 2 pairs of shoes?
a)
15
b)
40
c)
80
d)
10
59.
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?
a)
180
b)
23
c)
12
d)
60
60.

Which of the following is an example of combination?

a)

Form a passcode with 4 digits

b)

Students line up in a queue to assembly

c)

Choose 4 students in a class committee

d)

Choose the chairperson, secretary and treasurer in a club

Similar Resources on Wayground

Review (Lines, Slopes, Like Terms, etc.)

55 questions

Review (Lines, Slopes, Like Terms, etc.)

quiz

Worksheet

•

9th Grade - University

Metric Measurement: Linear

65 questions

Metric Measurement: Linear

quiz

Worksheet

•

4th Grade - University

IQ: AI THÔNG MINH HƠN HỌC SINH MẦM NON

62 questions

IQ: AI THÔNG MINH HƠN HỌC SINH MẦM NON

quiz

Worksheet

•

1st Grade - Professio...

SIMULADOR UNESUM 1

60 questions

SIMULADOR UNESUM 1

quiz

Worksheet

•

5th Grade - University

матем сессия

61 questions

матем сессия

quiz

Worksheet

•

University

discrete mathematics

60 questions

discrete mathematics

quiz

Worksheet

•

University

Real Numbers Test Quizizz

55 questions

Real Numbers Test Quizizz

quiz

Worksheet

•

8th Grade - University

PRUEBA ABSTRACTO

57 questions

PRUEBA ABSTRACTO

quiz

Worksheet

•

1st Grade - Professio...