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vinay1983: Legendary Member; Posts: 643; Joined: Wed Aug 14, 2013 4:27 amFollowed by: 7 members; Thanked: 48 times

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

You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!

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Source: Beat The GMAT — Problem Solving | Thu Sep 26, 2013 7:08 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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visheshchadha: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Wed Sep 25, 2013 9:48 am; Thanked: 1 times

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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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

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.

R A H U L

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