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# Ben and Ann are among 7 contestants from which 4

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Manager
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Ben and Ann are among 7 contestants from which 4 [#permalink]

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08 Feb 2008, 12:50
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Ben and Ann are among 7 contestants from which 4 semifinalists are to be selected. Of the diferent possible selections, how many contain neither Ben nor Ann?

A. 5
B. 6
C. 7
D. 14
E. 21
Manager
Joined: 01 Nov 2007
Posts: 144
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Re: PS - Combinatorics [#permalink]

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08 Feb 2008, 13:01
Could you please elaborate on the solution?

Thanks

eschn3am wrote:
5C4 = 5

Answer A
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Re: PS - Combinatorics [#permalink]

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08 Feb 2008, 13:08
JCLEONES wrote:
Could you please elaborate on the solution?

Thanks

eschn3am wrote:
5C4 = 5

Answer A

We have a pool of 7 people and we want to know how many ways we can form a group of 4 that does NOT include 2 of the members. Essentially, we're cutting the pool of 7 down to a pool of 5 and looking for the number of ways to choose 4.

5!/4!1! = 5
Re: PS - Combinatorics   [#permalink] 08 Feb 2008, 13:08
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# Ben and Ann are among 7 contestants from which 4

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