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Math Help - Combination

  1. #1
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    Question Combination

    I need to write this expression with one combination number: C(15,3)-C(16,2)=C(n,k) so I need to find n and k
    How can i get one from these two without using factorials?
    Last edited by Serillan; October 28th 2012 at 11:53 AM.
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  2. #2
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    Re: Combination

    Quote Originally Posted by Serillan View Post
    I need to write this expression with one combination number: C(15,3)-C(16,2)=C(n,k) so I need to find n and k
    How can i get one from these two without using factorials?
    I have though about this question since it was posted.
    The way it is written implies the use of Pascal's Identity
    \binom{N+1}{k}=\binom{N}{k-1}+\binom{N}{k}.

    But that lead nowhere that I can see.

    Now \binom{15}{3}-\binom{16}{2}=335.
    So I did a rather large computer search on various combinations \binom{N}{k} but found none to equal 335. I thought that finding one might give a clue as to how that identity might apply.
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