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Combinations - somewhat tricky

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Senior | Next Rank: 100 Posts
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by ellexay » Wed Feb 11, 2009 7:03 am
A committee of 6 is chosen from 8 men and 5 women so as to contain at least 2 men and 3 women. How many different committees could be formed if two of the men refuse to serve together?

(A) 3510
(B) 2620
(C) 1404
(D) 700
(E) 635





ANS - (E)
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Re: Combinations - somewhat tricky

by x2suresh » Wed Feb 11, 2009 8:10 am
ellexay wrote:A committee of 6 is chosen from 8 men and 5 women so as to contain at least 2 men and 3 women. How many different committees could be formed if two of the men refuse to serve together?

(A) 3510
(B) 2620
(C) 1404
(D) 700
(E) 635

No.of ways to chose 6 members comitte without restriction (two men refuse to server togethr)
= 8C2*5C4+8C3*5C3
= 700

No.of ways to chose 6 members with two men server together.
= 2C2 *5C4+ 2C2*6C1*5C3 = 5+60 = 65

Ans = 700-65 = 635

E.



ANS - (E)
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