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Math Help - Factorial Proof

  1. #1
    Junior Member
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    Oct 2009
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    Factorial Proof

    Hi everyone,

    Can anyone help me prove this factorial, or give me an idea as to why this might be true...

    (nx) *(mt-x) = (n+mt)


    That is, n choose x times m choose (t-x) is equal to n+m choose t.

    Thanks in advance!
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  2. #2
    Member
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    Bratislava
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    Thanks
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    Re: Factorial Proof

    Quote Originally Posted by KelvinScale View Post
    Hi everyone,

    Can anyone help me prove this factorial, or give me an idea as to why this might be true...

    (nx) *(mt-x) = (n+mt)


    That is, n choose x times m choose (t-x) is equal to n+m choose t.

    Thanks in advance!
    You probably forgotten to add the sum over all x. (Without the sum the formula is not true, as you can verify yourself by checking concrete examples.)

    With the sum it is Chu-Vandermonde identity:
    Vandermonde's identity - Wikipedia, the free encyclopedia
    Chu-Vandermonde Identity - ProofWiki
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