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?
Solution
Correct Answer: Option D
We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only).
Required number of ways = (7C3 x 6C2) + (7C4 x 6C1) + (7C5)
= (7 x 6 x 5)/( 3 x 2 x 1) x (6 x 5)/( 2 x 1) + (7C3 x 6C1) + (7C2)
= 525 + [{(7 x 6 x 5)/( 3 x 2 x 1)}x 6] + (7 x 6)/( 2 x 1)
= (525 + 210 + 21)
= 756.
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