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

Solution

Correct Answer: Option D

From a group of 7 men and 6 women, five persons are to be selected with at least 3 men. So we can have (5 men) or (4 men and 1 woman) or (3 men and 2 woman)

(5C5)+(5C4∗6C1)++(5C3∗6C2)

=[(7*6)/(2*1)]+[(7*6*5)/(3*2*1)*6]+[(7*6*5)/(3*2*1)*(6*5)/(2*1)]

=21+210+525

=756

Solution

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