# Permutations and Combinations Quiz Set 014

### Question 1

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 2

In how many ways can 6 prizes be given to 4 students if each of them is equally eligible?

A

1296.

B

1306.

C

1326.

D

1316.

Soln.
Ans: a

The first has 6 options, the second also has 6 options, and so on. This is expressed as 6 × 6 × 6 × 6, which evaluates to 1296.

### Question 3

How many four letter words, with all the letters different, can be formed out of the letters of the word 'AFTERSHOCK'?

A

5040.

B

5050.

C

5030.

D

5060.

Soln.
Ans: a

This word has 10 different letters. The number of possibilities is 10P4 = 5040.

### Question 4

From a group of 9 boys and 4 girls, in how many ways can 2 boys and 2 girls be selected?

A

216.

B

226.

C

206.

D

236.

Soln.
Ans: a

The required count is 4C2 × 9C2 = 216.

### Question 5

In how many ways can a secretary and general secretary be chosen from a committee of 13 members?

A

156.

B

161.

C

154.

D

157.

Soln.
Ans: a

The secretary can be any of the 13 members, the general-secretary can then be any of the (13 - 1) members. So the answer is 13 × (13 - 1) = 156.