From a group of 8 men and 7 women a committee consisting of 4 men and 3 women is to be formed.How many different committees. is possible if :
If everyone would serve with any of the others the answer would be
C(8,4)*C(7,3) = 70·35 = 2450
a) 2 of the men refuse to serve together?
From the 2450, we must subtract the number of ways those two men
serve togetner.
If they serve together, then we can choose the other 2 men that serve
with them in C(6,2) ways. The women are chosen C(7,3) ways, so the
number we must subtract from the 2450 is:
C(6,2)*C(7,3) = 15·35 = 525
Answer: 2450 - 525 = 1925 ways
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b) 2 of the women refuse to serve together?
From the 2450, we must subtract the number of ways those two women
serve togetner.
If they serve together, then we can choose the 1 other woman to
serve with them in 5 ways. The men are chosen C(8,4) = 70 ways, so
the number we must subtract from the 2450 is
5·70 = 350
Anser: 2450 - 350 = 2100 ways
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c) 1 man and 1 woman refuse to serve together?
From the 2450 we must subtract the cases where that man and woman
serve together. In those cases we choose 3 men from the other 7 and
2 women from the other 6. so the number we must subtract is:
C(7,3)*C(6,2) = 35·15 = 525
Answer: 2450 - 525 = 1925 ways
Edwin