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?

A. 564

B. 645

C. 735

D. 756

View Answer

Correct Answer :
756

Explanation :

Committee may have (3 men and 2 women) or (4 men and 1 women) or (5 men)

Required number of ways = (7C3 x 6C2) + (7C4 x 6C1) + (7C5)

As nCr = nC(n-r), then required number of ways can be written as

= (7C3 x 6C2) + (7C3 x 6C1) + (7C2)

= (525 + 210 + 21)

= 756

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