# Permutations and Combinations Quiz Set 016

### Question 1

The letters of the word 'VIOLET' 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

Out of given 6 consonants and 4 vowels, how many words can be formed that contain 3 consonants and 2 vowels or 3 vowels and 2 consonants?

A

21600.

B

21610.

C

21590.

D

21620.

Soln.
Ans: a

We can make the selection in 4C3 × 6C2 + 4C2 × 6C3 ways. But the five members can themselves be arranged in 5! ways. So the number of words is 120 × (4C3 × 6C2 + 4C2 × 6C3) = 21600.

### Question 3

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.

### Question 4

From a group of 6 boys and 7 girls, in how many ways can 2 boys and 2 girls be selected?

A

315.

B

325.

C

305.

D

335.

Soln.
Ans: a

The required count is 7C2 × 6C2 = 315.

### Question 5

How many possible outcomes are there if a die with 5 faces is cast and then a coin with 2 sides is tossed?

A

10.

B

15.

C

8.

D

11.

Soln.
Ans: a

The die can fall in 5 different ways, and a coin in 2 ways. So the outcomes are 2 × 5 = 10. This Blog Post/Article "Permutations and Combinations Quiz Set 016" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2020-02-07. Published on: 2016-05-08