# Permutations and Combinations Quiz Set 006

### Question 1

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

From a group of 5 boys and 7 girls, in how many ways can 2 boys and 2 girls be selected?

A

210.

B

220.

C

200.

D

230.

Soln.
Ans: a

The required count is 7C2 × 5C2 = 210.

### Question 3

What is the value of 7C2?

A

21.

B

31.

C

11.

D

41.

Soln.
Ans: a

7C2 is \${7 !}/{(7 - 2) ! × 2 !}\$ = 21.

### Question 4

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

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 5

What is the value of 6P3?

A

120.

B

130.

C

110.

D

140.

Soln.
Ans: a

6P3 is \${6 !}/{(6 - 3) !}\$ = 120.

This Blog Post/Article "Permutations and Combinations Quiz Set 006" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2017-05-17.

Posted by Parveen(Hoven),
Aptitude Trainer