Free Printable Permutation vs. Combination

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)

$_3C_8$

Permutation vs. Combination

Total questions: 20

Worksheet time: 7mins

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