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How many distinct groupings of 2 tribes are possible?

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by Vemuri » Sun Mar 22, 2009 5:59 am
Ten telegenic contestants with a variety of personality disorders are to be divided into 2 tribes of 5 members each, tribe A and tribe B, for a competition. How many distinct groupings of 2 tribes are possible?

A. 120
B. 126
C. 252
D. 1200
E. 1260
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Re: How many distinct groupings of 2 tribes are possible?

by Brent@GMATPrepNow » Sun Mar 22, 2009 6:45 am
Vemuri wrote:Ten telegenic contestants with a variety of personality disorders are to be divided into 2 tribes of 5 members each, tribe A and tribe B, for a competition. How many distinct groupings of 2 tribes are possible?

A. 120
B. 126
C. 252
D. 1200
E. 1260
We can break this task into two stages:
1. Choose 5 contestants and place them in Tribe A
2. Place the remaining 5 contestants in Tribe B

We can accomplish stage A in 10C5 ways (252)
Stage B is accomplished in 1 way
The total number is 252x1=252 (C)
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