Permutations and Combinations Quiz Set 006

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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.


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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


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