Question 800828
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 :
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If everyone would serve with any of the others the answer would be

C(8,4)*C(7,3) = 70·35 = 2450
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a) 2 of the men refuse to serve together?
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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?
<pre>
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?
<pre>
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</pre>