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Math Help - need help, on greatet integer function.

  1. #1
    Junior Member
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    need help, on greatet integer function.

    Show that (2a)!(2b)!/(a!b!(a + b)!) is an integer.
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  2. #2
    Senior Member
    Joined
    Apr 2009
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    Atlanta, GA
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    408

    A "verbal" proof?

    Rearranging, you get \frac{(2a)!}{a!}*\frac{(2b)!}{b!}*\frac{1}{(a+b)!}

    Which equals \frac{(_{2a}P_a)*(_{2b}P_b)}{(a+b)!}

    In plain English, you are picking a objects from 2a options and b objects from 2b options with regard to order. Thus, the (a+b)! term is simply dividing out all possible orderings of your a+b objects.

    I am sure someone can come up with a formal proof, but this at least should be convincing
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