Free Printable Permutations and Combinations

Worksheets

Permutations and Combinations

Total questions: 20

Worksheet time: 1hrs 25mins

Name

Class

Date

How many ways can you arrange 2 letters from the word
S Q U A R E?

140

320

Student council has 24 members. In how many different ways can a president, vice-president, treasurer, historian, and secretary be selected?

5,100,480

42,504

5.17 x 10²¹

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?

3360

560

4080

680

Find the possibilities when a group of 15 people are going to run a race. The top 5 finishers advance to the finals.

1.3 x 10¹²

120

3003

360,360

Your history teacher randomly chooses 2 out of 18 students to give an impromptu debate on freedom of press in the high school news paper. What is the probability that both you and your best friend are chosen to give the debate?

1/153

1/306

2/153

40/51

When does the order in which you are choose matter?

Combination

Permutation

How many 5-digit (numerical) passwords are possible for the school email system if the first digit cannot be 0?

11,424,400

10,967,424

9000

90,000

Choosing 3 toppings for your sundae out of a list of 15.

Permutation

Combination

Neither

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?

12,650

303,600

100

254

10.

Sarah plays softball over the summer. If there are 10 players on the team, how many ways can the coach make a batting order that includes all players?

3628800

100

1814400

11.

The Nebraska license plate has 6 characters, each one filled with a number (0-9) or a letter. How many license plates are possible?

2176782336

1402410240

12.

Justin took a quiz with five multiple choice (A-D) and five true/false questions. How many different ways can he answer the questions?

1024

32768

13.

Brianna’s school day consists of six classes. How many different ways can her schedule be arranged?

720

100

500

14.

If Lucas owns 11 hoodies,how many ways can he choose four to bring on vacation?

7920

330

121

15.

How many different arrangements can be made from COLLEGE?

720

1260

35280

16.

There are 10 men and 6 women working at a company. A hiring committee of 4 staff members is selected by a supervisor.

What is the probability that the committee is made up of 3 women and 1 man?

10/91

1/20

3/16

36/91

17.

You are dealt 5 cards from a standard deck of playing cards. What is the probability you are dealt a flush?

**A flush is all 5 cards of the same suit (order does not matter).

1/1287

1/2598960

1287/2598960

5/52

18.

How many different permutations can be made from the letters of the word COMMUNICATION?

(a)

19.

What is the probability of getting exactly two heads in four flips of a fair coin?

$\frac{3}{8}$

$\frac{1}{4}$

$\frac{1}{2}$

$\frac{5}{16}$

20.

There are ten toppings available to make an ice cream sundae. How many different sundaes can Lala make if she chooses two toppings?

100 %

Permutations and Combinations

Total questions: 20

Worksheet time: 1hrs 25mins

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