Easy
Probability
Level
3
From a group of 6 men and 5 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?
The answer is 281.
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1 solution
There can be 3 cases. CASE I- 3 men from 6 men and remaining 2 women from 5 women. Therefore total no. of ways possible in this case= 6c3 x5c2 = 20 x10=200 CASE II- 4 men from 6 men and remaining 1 woman from 5 women. Therefore total no. of ways possible in this case= 6c4x5c1 = 15x5=75 CASE III- 5 men from 6 men and no woman. Therefore total no. of ways possible in this case= 6c5 x5c0 = 6x1=6 Therefore total ways possible in all=200+75+6= 281