Help on solving a combination problem

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crackgmat007: Legendary Member; Posts: 882; Joined: Fri Feb 20, 2009 2:57 pmFollowed by: 1 member; Thanked: 15 times; GMAT Score:690

by crackgmat007 » Mon Apr 13, 2009 8:39 pm

Since only Tom or Jerry can be on the committe, I considered Tom & Jerry as 'one' for calucating the combinations. Hence, 6C3 = 20.

Answer seems to be C (30)...am I missing something?

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Source: Beat The GMAT — Problem Solving | Mon Apr 13, 2009 8:39 pm

kirvar: Junior | Next Rank: 30 Posts; Posts: 21; Joined: Fri Mar 13, 2009 9:35 pm; Thanked: 1 times

by kirvar » Mon Apr 13, 2009 9:06 pm

Number of groups with only Tom: 5C2 = 10

Number of groups with only Jerry: 5C2 = 10

Number of groups with neither Jerry nor Tom: 5C3 =10

Total = 30

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Mon Apr 13, 2009 9:09 pm

Tom and Jerry are 2 different persons.

One way to do it is to first find the total number of 3 member sub committes possible from 7 people

7C3 = 35

Then find the number of subcomitees in which Tom and Jerry will be there.

2c2( which iequals 1) * 5c1 (once u choose Tom and Jerry u have 5 persons remaining to choose 1 from) = 5

Subtract 2 from 1 which will give u the number of 3 member commitees where Tom and Jerry will not be there

35 - 5

= 30

Regards,
CR

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