From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done? : Crackverbal Support

From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done? Print

Modified on: Tue, 12 Oct, 2021 at 4:05 PM

Concept: The question tests on basics of Selection.

Solution:

At least 3 men in the question implies 3men and 2 women Or 4 men and 1 woman Or 5 men and 0 women.

The Or condition implies an addition here after every case is computed.

Hence

(7C3)*(6C2) to select 3men and 2 women or

(7C4)*(6C1) to select 4 men and 1 woman or

(7C5)*(6C0) to select 5 men and 0 women.

Adding all we have (7C3)*(6C2) + (7C4)*(6C1) + (7C5)*(6C0)

= 525 +210+ 21

= 756 (Option D)

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From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done? Print

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