# Combination Problem

• Jul 30th 2011, 04:54 PM
KingNathan
Combination Problem
Hi, I am studying for the GMAT and there is an example in one of my test prep books that does not make sense to me.

"a man has 5 shirts. If he has to bring 2 shirts, how many possible arrangements are there? Order does not matter"

The formula it says is C(5,3) 5!/(5-3)!*3!

What I can't understand is why m=3 instead of 2. If it's arrangements of 2 shirts, why isn't it C(5,2) 5!/(5-2)!*2!
• Jul 30th 2011, 05:23 PM
Plato
Re: Combination Problem
Quote:

Originally Posted by KingNathan
Hi, I am studying for the GMAT and there is an example in one of my test prep books that does not make sense to me.
"a man has 5 shirts. If he has to bring 2 shirts, how many possible arrangements are there? Order does not matter"
The formula it says is C(5,3) 5!/(5-3)!*3!
What I can't understand is why m=3 instead of 2. If it's arrangements of 2 shirts, why isn't it C(5,2) 5!/(5-2)!*2!

They are the same.
$\displaystyle \binom{5}{2}=\frac{5!}{2!(5-2)!}=\binom{5}{3}=\frac{5!}{3!(5-3)!}$
• Jul 30th 2011, 05:42 PM
KingNathan
Re: Combination Problem
Quote:

Originally Posted by Plato
They are the same.
$\displaystyle \binom{5}{2}=\frac{5!}{2!(5-2)!}=\binom{5}{3}=\frac{5!}{3!(5-3)!}$

Thanks, however, on the GMAT, the answers will not be the same. I need to know where the 3 came from as m? I see 5 possible selections making n=5, an then 2 shirts per arrangement, so why isn't m=2 instead of 3?
• Jul 31st 2011, 04:08 AM
mr fantastic
Re: Combination Problem
Quote:

Originally Posted by KingNathan
Thanks, however, on the GMAT, the answers will not be the same. I need to know where the 3 came from as m? I see 5 possible selections making n=5, an then 2 shirts per arrangement, so why isn't m=2 instead of 3?

The solution should have said C(5, 2).
• Jul 31st 2011, 04:36 AM
islam
Re: Combination Problem
the 3 comes from the fact that selecting 2 shirts of 5 means "unselecting'' 3 shirts of 5
which is equivalent
• Jul 31st 2011, 12:23 PM
mr fantastic
Re: Combination Problem
Quote:

Originally Posted by islam
the 3 comes from the fact that selecting 2 shirts of 5 means "unselecting'' 3 shirts of 5
which is equivalent

Although correct, the GMAT answer is going to confuse many students. Answers often suggest the approach - in this case it is obvious where C(5, 2) comes from, it is much less obvious (and this thread is a case in point) where C(5, 3) comes from. 'Unselecting' is not the natural approach for this question and beginners will find the GMAT answer confusing. In my opinion, it is a correct but not a good answer.