# Permutations and Combinations Quiz Set 005

### Question 1

What is the value of 8C3?

A

56.

B

66.

C

46.

D

76.

Soln.
Ans: a

8C3 is \${8 !}/{(8 - 3) ! × 3 !}\$ = 56.

### Question 2

What is the value of 5P3?

A

60.

B

70.

C

50.

D

80.

Soln.
Ans: a

5P3 is \${5 !}/{(5 - 3) !}\$ = 60.

### Question 3

From a group of 9 men and 5 women, in how many ways can 3 men and 2 women or 2 men and 3 women be selected?

A

1200.

B

1210.

C

1190.

D

1220.

Soln.
Ans: a

The required count is 5C3 × 9C2 + 5C2 × 9C3 = 1200.

### Question 4

The letters of the word 'ORANGE' have to be arranged such that the vowels occupy only the odd positions. How many different ways are possible?

A

36.

B

46.

C

26.

D

56.

Soln.
Ans: a

This word has 6 letters, out of which 3 are consonants and 3 are vowels. The vowels have to occupy three fixed odd positions. We can place 3 vowels in first odd place, 2 in second odd place and 1 in the third odd place, giving 3 × 2 × 1 = 6 permutations. This will be done with the consonants also. So the total possibilities are 6 × 6 = 36.

### Question 5

In how many ways can 3 letter words be formed by using a given set of 12 consonants?

A

1320.

B

1325.

C

1318.

D

1321.

Soln.
Ans: a

The first place can get any of the 12 consonants, the second place can then get (12 - 1), and likewise. This is expressed as 12 × 11 × 10, which evaluates to 1320.