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Permutation and Combination - General Aptitude

Q1:

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

E None of these

ANS:D - 756

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 x 6 x 5 + (7C3 x 6C1) + (7C2)
3 x 2 x 1 2 x 1
 
= 525 + 7 x 6 x 5 x 6 + 7 x 6
3 x 2 x 1 2 x 1
  = (525 + 210 + 21)
  = 756.