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gmatnmein2010: Master | Next Rank: 500 Posts; Posts: 185; Joined: Thu Feb 04, 2010 3:06 am; Thanked: 6 times

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by gmatnmein2010 » Mon Feb 08, 2010 5:36 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

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Source: Beat The GMAT — Problem Solving | Mon Feb 08, 2010 5:36 am

harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 am; Location: India; Thanked: 64 times; Followed by:6 members; GMAT Score:760

by harsh.champ » Mon Feb 08, 2010 5:58 am

gmatnmein2010 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

Taking cases
Case 1:- 3men,3 women 8C3x 5C3 - 8C1 x 5C3
Case 2 :-2 men,4 women 8C2 x 5C4 - 6C0 x 5C4

Remove the cases when those 2 men are there

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thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 am; Thanked: 137 times; Followed by:5 members

by thephoenix » Mon Feb 08, 2010 6:45 am

Two cases: 2 men and 4 women OR 3 men and 3 women.
Ways to chose 6 members committee without restriction (two men refuse to server together)=8C2*5C4+8C3*5C3 = 700
Ways to chose 6 members with two men serve together=2C2*5C4+2C2*6C1*5C3=5+60=65
700-65 = 635

imo e

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Warlock007: Senior | Next Rank: 100 Posts; Posts: 41; Joined: Sat Jan 08, 2011 7:34 am; Thanked: 2 times; Followed by:1 members

by Warlock007 » Thu Mar 10, 2011 12:07 pm

harsh.champ wrote:
gmatnmein2010 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
Taking cases
Case 1:- 3men,3 women 8C3x 5C3 - 8C1 x 5C3
Case 2 :-2 men,4 women 8C2 x 5C4 - 6C0 x 5C4

Remove the cases when those 2 men are there

abe Case 1 mein 8C1 ki jagah 6C1 kar mere bhai
baaki sab theek hai
jiyoooooooo