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# In a class comprising boys and girls, there were 45 hand

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Senior Manager
Joined: 29 Jan 2007
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In a class comprising boys and girls, there were 45 hand [#permalink]  23 Mar 2007, 14:58
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In a class comprising boys and girls, there were 45 hand shakes amongst the girls and 105 hand shakes amongst the boys. How many hand shakes took place between a boy and a girl, if each member of the class shook hands exactly once with every other student in the class?

25
15
150
300
24
GMAT Instructor
Joined: 04 Jul 2006
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If there are n girls, there are n(n-1)/2 handshakes among the girls, so n(n-1)=90 and n=10. Similarly, there are 15 boys. Thus there are 25 people and 25(24)/2 =300 handshakes in all 300-105-45=150 of which took place between children of opposite sexes
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150

Number of Girls:
nC2=45 --> n!/2!(n-2)!=45 --> Solve for n: n(n-1)!/2!=45 --> n^2-n=90
n=10

Same for the Boys and you get 15

10*15=150
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Re: PS Permutation, Combination [#permalink]  23 Mar 2007, 16:38
kyatin wrote:
In a class comprising boys and girls, there were 45 hand shakes amongst the girls and 105 hand shakes amongst the boys. How many hand shakes took place between a boy and a girl, if each member of the class shook hands exactly once with every other student in the class?

25
15
150
300
24

# of girls can be found out by 45 = G choose 2 which gives G = 10
# boys similarly can be found out by 105 = B choose 2 which gives B = 15

# of handshakes between boys and girts = 10 * 15 = 150
Re: PS Permutation, Combination   [#permalink] 23 Mar 2007, 16:38
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