Free Printable Permutation and Combination

1.

What is the formula for permutation?

a)

$n_{P_{r\ }=\ \frac{n!}{\left(n-r\right)!}}$

b)

$n_{P_{r\ }=\ \frac{n!}{r!\left(n-r\right)!}}$

c)

$n_{C_{r\ }=\ \frac{n!}{r!\left(n-r\right)!}}$

d)

$n_{C_{r\ }=\ \frac{n!}{\left(n-r\right)!}}$

2.

What is the formula for combination?

a)

$n_{P_{r\ }=\ \frac{n!}{r!\left(n-r\right)!}}$

b)

$n_{C_{r\ }=\ \frac{n!}{r!\left(n-r\right)!}}$

c)

$n_{P_{r\ }=\ \frac{n!}{\left(n-r\right)!}}$

d)

$n_{C_{r\ }=\ \frac{n!}{\left(n-r\right)!}}$

3.

Find the number of words, with or without meaning, that can be formed with the letters of word “CHAIR”?

a)

120

b)

3125

c)

5

d)

25

4.

Mariam wants to order a sandwich with two of the following ingredients: mushroom, eggplant, tomato, and avocado. How many different sandwiches can Mariam choose?

a)

8

b)

6

c)

4

d)

2

5.

How many ways can you arrange 2 letters from the word SQUARE?

a)

45

b)

320

c)

30

d)

140

6.

A Mathematics test contains five different questions labelled A, B, C, D, and E. You are supposed to choose 2 to answer. How many different ways are there to do this?

a)

5

b)

15

c)

10

d)

15

7.

There are _ ways can be arranged from the letters "MATH"

(a)

8.

How many 2-digit numbers can you make using the digits 1, 2, 3, and 4 without repeating the digits?

a)

24

b)

90

c)

12

d)

100

9.

A group of 4 men and 3 ladies are to be seated in a row for a photo session. If the men and ladies want to be seated alternately, calculate the number of different arrangements?

a)

24

b)

144

c)

64

d)

12

10.

Calculate the number of ways to arrange 9 books of different tittles on a book rack?

a)

31

b)

362880

c)

368280

d)

45

11.

Six friends are going to play a ball game. Each team has 3 players. How many different team combinations are possible?

a)

120

b)

6

c)

18

d)

20

12.

There are 35 teachers in a school. In how many different ways one principal and one vice principal can be chosen?

a)

1160

b)

1170

c)

1180

d)

1190

13.

A code is to be formed using A, B, C, D, E, F, 5, 6, 7 and 8. If the code must consist of 4 letters followed by 3 digits numbers, how many codes can be formed without repetition?

a)

604800

b)

8640

c)

3628800

d)

144

14.

A physical education class contains 20 students. In how many ways can a swimming instruction group be formed consisting of 5 students?

a)

5168

b)

7752

c)

15504

15.

You are ordering a triple-scoop ice-cream cone. There are 18 flavours to choose from and you don’t care which flavor is on the top, middle, or bottom. How many different ways can you select a triple-scoop ice-cream cone?

a)

816

b)

54

c)

4896

16.

A basketball team has 12 members who can play any position. There are _ different ways for the coach to choose 5 starting players.

(a)

17.

A freezer contains 24 frozen entrees with only one serving of each one. In how many ways can a family of 4 diners select their entrees?

a)

14626

b)

12626

c)

10626

Permutation and Combination

Total questions: 17

Worksheet time: 26mins

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