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Math Help - Combination Problem

  1. #1
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    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!
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  2. #2
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    Re: Combination Problem

    Quote Originally Posted by KingNathan View Post
    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.
    \binom{5}{2}=\frac{5!}{2!(5-2)!}=\binom{5}{3}=\frac{5!}{3!(5-3)!}
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  3. #3
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    Re: Combination Problem

    Quote Originally Posted by Plato View Post
    They are the same.
    \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?
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    Re: Combination Problem

    Quote Originally Posted by KingNathan View Post
    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).
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  5. #5
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    Re: Combination Problem

    the 3 comes from the fact that selecting 2 shirts of 5 means "unselecting'' 3 shirts of 5
    which is equivalent
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    Re: Combination Problem

    Quote Originally Posted by islam View Post
    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.
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