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Teams

by vinay1983 » Thu Sep 26, 2013 7:08 am
Jill is dividing her ten-person class into two teams of equal size for a basketball game. If no one will sit out, how many different match-ups between the two teams are possible?

A. 10
B. 25
C. 126
D. 252
E. 630
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by Brent@GMATPrepNow » Thu Sep 26, 2013 8:16 am
vinay1983 wrote:Jill is dividing her ten-person class into two teams of equal size for a basketball game. If no one will sit out, how many different match-ups between the two teams are possible?

A. 10
B. 25
C. 126
D. 252
E. 630
Let's say we have Team Blue and Team Red. Notice that once we select 5 people to be on Team Blue, the other 5 people must automatically be on Team Red.

In how many ways can we select 5 people to be on Team Blue?
Since the order in which we select the 5 people does not matter, we can use combinations.
We can select 5 people from 10 people in 10C5 ways (= 252 ways)

So, there are 252 different ways to select 5 people to be on Team Blue and 5 people to be on Team Red?

IMPORTANT: Notice that Team Blue = {A,B,C,D,E} and Team Red = {F,G,H,I,J} is EXACTLY THE SAME as team Blue = {F,G,H,I,J} and Team Red = {A,B,C,D,E}.
In fact, we have inadvertently counted each possible configuration TWICE.

So, to get the correct answer, we must take 252 and divide by 2 to get 126

Answer: C

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by visheshchadha » Fri Sep 27, 2013 11:32 am
It's easy. You only have to do the Selection. If we select one of the two groups, the other group is selected by default.

Therefore number of ways of selecting 5 people from 10 = C(10, 5) = 252
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by theCodeToGMAT » Fri Sep 27, 2013 8:30 pm
visheshchadha wrote:It's easy. You only have to do the Selection. If we select one of the two groups, the other group is selected by default.

Therefore number of ways of selecting 5 people from 10 = C(10, 5) = 252
It can't be 252.. Brent has beautifully explained the reason in his solution post,which is above your post.
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