Asked by Silverln
A committee of 4 is to be selected from 5 women and 7 men.In how many ways;a)Can this committee be selected? b)Can this committee be selected if 3 men must be included c)Can the committee be selected if at least 3 women must be included?
Answers
Answered by
Reiny
5 women
7 men, choose 4
a) number of ways with no restriction
= C(12, 4) = 495
b) must be 3 men and 1 woman
= C(7,3) x C(5,1) = 35 x 5 = 175
c) at least 3 women ---> 3 women or 4 women
= C(5,3) x C(7,1) + C(5,4) x C(7,0)
= 10x7 + 5x1
= 75
7 men, choose 4
a) number of ways with no restriction
= C(12, 4) = 495
b) must be 3 men and 1 woman
= C(7,3) x C(5,1) = 35 x 5 = 175
c) at least 3 women ---> 3 women or 4 women
= C(5,3) x C(7,1) + C(5,4) x C(7,0)
= 10x7 + 5x1
= 75
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