Free Printable Permutations and Combinations

1.

How many ways can you choose 15 oranges from a crate of 60?

PERMUTATION or COMBINATION? Which calculation is correct?

a)

$_{60}P_{15}$

b)

$_{15}C_{60}$

c)

$_{15}P_{60}$

d)

$_{60}C_{15}$

2.

How many ways can you choose 6 person dodge ball team out of 20 participants?

PERMUTATION or COMBINATION? Which calculation is correct?

a)

$_{20}P_6$

b)

$_{20}C_6$

c)

$_6P_{20}$

d)

$_6C_{20}$

3.

How many ways can you list your 4 favorite cheesecakes, in order, off a menu of 15 options?

PERMUTATION or COMBINATION? Which calculation is correct?

a)

$_4P_{15}$

b)

$_4C_{15}$

c)

$_{15}P_4$

d)

$_{15}C_4$

4.

How many ways can you set a 3-digit lock using the numbers 6, 2 and 4?

PERMUTATION or COMBINATION? Which calculation is correct?

a)

$_3P_3$

b)

$_3C_3$

c)

$_3P_1$

d)

$_3C_1$

5.

In how many ways can the batting order for nine players on a 16 person team be chosen?

PERMUTATION or COMBINATION? Which calculation is correct?

a)

$_{16}P_9$

b)

$_{16}C_9$

c)

$_9P_{16}$

d)

$_9C_{16}$

6.

Kim has homework in five subjects. In how many ways can she complete her homework?

PERMUTATION or COMBINATION? Which calculation is correct?

a)

$_5P_1$

b)

$_5C_1$

c)

$_5P_5$

d)

$_5C_5$

7.

You and 2 friends choose 3 out of 5 appetizers to share. How many ways can you do this?

PERMUTATION or COMBINATION? Which calculation is correct?

a)

$_5P_3$

b)

$_5C_3$

c)

$_3P_5$

d)

$_3C_5$

8.

A crayon box has 6 shades of red. How many ways could you choose 3 shades to color a bird?

PERMUTATION or COMBINATION? Which calculation is correct?

a)

$_6P_3$

b)

$_6C_3$

c)

$_3P_6$

d)

$_3C_6$

9.

How many ways can you choose a President, VP and Secretary from an 8 person committee?

PERMUTATION or COMBINATION? Which calculation is correct?

a)

$_3P_8$

b)

$_3C_8$

c)

$_8P_3$

d)

$_8C_3$

10.

How many handshakes are there when 50 men at a meeting shake hands with everyone else (in non-COVID times)?

PERMUTATION or COMBINATION? Which calculation is correct?

a)

$_{50}P_{50}$

b)

$_{50}C_{50}$

c)

$_{50}P_2$

d)

$_{50}C_2$

11.

In how many ways can you choose 3 out of 9 toppings from a salad bar?

PERMUTATION or COMBINATION? Which calculation is correct?

a)

$_9P_3$

b)

$_9C_3$

c)

$_3P_9$

d)

$_3C_9$

12.

How many ways can you file 12 tabbed dividers, one after another, in a 3-ring binder?

PERMUTATION or COMBINATION? Which calculation is correct?

a)

$_{12}P_{12}$

b)

$_{12}C_{12}$

c)

$_{12}P_3$

d)

$_{12}C_3$

13.

In how many ways can 10 students out of 34 be chosen to attend a conference?

PERMUTATION or COMBINATION? Which calculation is correct?

a)

$_{34}P_{10}$

b)

$_{34}C_{10}$

c)

$_{10}P_{34}$

d)

$_{10}C_{34}$

14.

How many 8-digit codes can be made for a lock (no repeated digits)?

PERMUTATION or COMBINATION? Which calculation is correct?

a)

$_8P_8$

b)

$_8C_8$

c)

$_{10}P_8$

d)

$_{10}C_8$

15.

How many ways can a local painter display 4 out of 8 of his favorite paintings?

PERMUTATION or COMBINATION? Which calculation is correct?

a)

$_8P_4$

b)

$_8C_4$

c)

$_4P_8$

d)

$_4C_8$

16.

You have seven new shows to watch on your DVR. In how many ways can you watch 5 of the shows?

PERMUTATION or COMBINATION? Which calculation is correct?

a)

$_7P_5$

b)

$_7C_5$

c)

$_5P_7$

d)

$_5C_7$

17.

How many ways can you arrange 4 songs on a playlist?

PERMUTATION or COMBINATION? Which calculation is correct?

a)

$_4P_4$

b)

$_4C_4$

c)

$_4P_1$

d)

$_4C_1$

18.

How many ways can you choose 4 equal prize winners from a group of 15 attendees?

PERMUTATION or COMBINATION? Which calculation is correct?

a)

$_4P_{15}$

b)

$_4C_{15}$

c)

$_{15}P_4$

d)

$_{15}C_4$

19.

In how many ways can the word TREE be arranged?

PERMUTATION or COMBINATION? Which calculation is correct?

a)

$_4P_4\ \ \div\ 2$

b)

$_4C_4\ \ \div\ 2$

c)

$_4P_4$

d)

$_4C_4$

20.

How many ways can 8 runners finish in 1st, 2nd or 3rd place?

PERMUTATION or COMBINATION? Which calculation is correct?

a)

$_8P_3$

b)

$_8C_3$

c)

$_3P_8$

d)

$_3C_8$

21.

How many ways can you file 12 tabbed dividers, one after another, in a 3-ring binder?

a)

Permutation

b)

Combination

22.

In how many ways can you choose a 6 person dodge ball team out of 20 participants?

a)

Permutation

b)

Combination

23.

How many ways can 8 runners finish in 1st, 2nd, or 3rd place?

a)

Permutation

b)

Combination

24.

How many 8 digit codes can be made for a lock?

a)

Permutation

b)

Combination

25.

In how many ways can the letters of the word TREE be arranged?

a)

Permutation

b)

Combination

26.

In how many ways can 10 students out of 34 be chosen to attend a conference?

a)

Permutation

b)

Combination

27.

How many ways can you arrange 4 songs on a playlist?

a)

Permutation

b)

Combination

28.

How many ways can you choose a President, VP, and Secretary from an eight person committee?

a)

Permutation

b)

Combination

29.

In how many ways can you choose three out of nine toppings from a salad bar?

a)

Permutation

b)

Combination

30.

In how many ways can you list your four favorite cheesecakes, in order, off a menu of 15 options?

a)

Permutation

b)

Combination

31.

How many ways can you choose 4 equal prize winners from a group of 15 attendees?

a)

Permutation

b)

Combination

32.

How many ways can you set a 3-digit lock using the numbers 6, 2, and 4?

a)

Permutation

b)

Combination

33.

A crayon box has 6 shades of red. How many ways could you choose 3 shades to color a bird?

a)

Permutation

b)

Combination

34.

How many handshakes are there when 50 men at a meeting shake hands with everyone else?

a)

Permutation

b)

Combination

35.

How many ways can you select 15 oranges out of a crate of 60?

a)

Permutation

b)

Combination

36.

In how many ways can the batting order for nine players on a 16 person team be chosen?

a)

Permutation

b)

Combination

37.

You and two friends choose 3 appetizers out of 5 appetizers to share. How many ways can you do this?

a)

Permutation

b)

Combination

38.

Kim has homework in five subjects. In how many ways can she complete her homework?

a)

Permutation

b)

Combination

39.

A group of 40 people are going to run a race. The top three runners earn gold, silver, and bronze medals.

a)

57,635

b)

177,840

c)

9,880

d)

59,280

40.

Selecting which ten players will be in the batting order on a 12 person team.

a)

77

b)

66

c)

264

d)

239,500,800

41.

Aliyah has homework assignments in seven subjects. She only has time to do five of them.

a)

28

b)

21

c)

19

d)

7

42.

A team of 14 softball players needs to choose three players to refill the water cooler.

a)

728

b)

2,184

c)

398

d)

364

43.

Castel and Maria are planning trips to three countries this year. There are 8 countries they would like to visit. One trip will be one week long, another two days, and the other two weeks.

a)

336

b)

112

c)

67

d)

56

44.

How many different ways can the letters of the word "MATH" be arranged?

45.

In how many ways can a committee of 3 members be selected from a group of 10 people?

46.

Using the counting principle, how many different two-letter codes can be created using the letters A, B, C, and D without repeating letters?

47.

If there are 4 different books on mathematics, 3 different books on physics, and 2 different books on chemistry, in how many ways can the books be arranged on a shelf if the books on the same subject must be kept together?

48.

How many different ways can a president, vice-president, and secretary be chosen from a club of 10 members?

49.

In how many ways can a 4-member relay team be selected from a group of 8 athletes?

a)

70

b)

1680

c)

24

d)

56

50.

There are ten toppings available to make an ice cream sundae. How many ways can Lala choose two?

51.

In a Permutation the order of the outcomes (a) , but in a Combination the order (b)

Choose from the below words

matters

doesn't matter

52.

Match the following

a)

Fundamental Counting Principle

1.

Ways to choose items after the first item has been chosen.

b)

Factorial

2.

the product of the natural numbers less than or equal to the number!

c)

Permutation

3.

a selection of a group of objects in which order is important

d)

Combination

4.

a grouping of items in which order does not matter

e)

Probability

5.

the measure of how likely an event is to occur

Permutations and Combinations

Total questions: 52

Worksheet time: 40mins

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