Discussion of Question with ID = 004 under Permutations-and-Combinations

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Question

Out of given 7 consonants and 3 vowels, how many words can be formed that contain 3 consonants and 2 vowels or 3 vowels and 2 consonants?

A

15120.

B

15130.

C

15110.

D

15140.

Soln.
Ans: a

We can make the selection in 3C3 × 7C2 + 3C2 × 7C3 ways. But the five members can themselves be arranged in 5! ways. So the number of words is 120 × (3C3 × 7C2 + 3C2 × 7C3) = 15120.

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