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# PS - combination

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Manager
Joined: 27 May 2008
Posts: 193

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16 Mar 2009, 06:44
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A group contains 7 boys and some girls. The number of teams of 5 comprising 3 boys and 2 girls is 525. How many girls are in the group?

5
6
7
9
11

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CEO
Joined: 17 Nov 2007
Posts: 3486
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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16 Mar 2009, 11:44
B
$$525 = C^7_3 * C^x_2=\frac{7*6*5}{3*2}*\frac{x*(x-1)}{2}$$

x(x-1)=30 ---> x=6
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Manager
Joined: 19 Aug 2006
Posts: 226

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16 Mar 2009, 13:10
selvae wrote:
A group contains 7 boys and some girls. The number of teams of 5 comprising 3 boys and 2 girls is 525. How many girls are in the group?

5
6
7
9
11

boys=> 7!/4!3!=35
525=35*g, where g is the number of teams comprising of girls only, so g=525/35=15 girls
We know that 15 = g!/(g-2)!2! , where g is the total number of girls available.

Solving backwards, and plugging the 1st available answer 5 quickly shows us that the number of girls should be a bit higher. Trying the number 6 works: 6!/4!2!=15

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Re: PS - combination   [#permalink] 16 Mar 2009, 13:10
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