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### Discussion :: Permutation and Combination

1. 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?

2.  A. 564 B. 645 C. 735 D. 756 E. None of these

Explanation :

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)

=$$[ \frac { 7*6*5 } { 3*2*1 }$$ x $$\frac { 6*5 } { 2*1 }]$$ +(7C3 x 6C1) + (7C2)

= 525+$$[ \frac { 7*6*5 } { 3*2*1 }$$x6]+$$[\frac { 7*6 } { 2 *1} ]$$

=(525 + 210 + 21)

= 756

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