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Math Help - Binomial Coefficients

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    Binomial Coefficients

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  2. #2
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    Note that (n-2)(n-3).......1 = (n-2)!

    Now consider \frac{n!}{2!(n-2)!}

    = \frac{n(n-1)(n-2)(n-3).......1}{2!(n-2)!}

    = \frac{n(n-1)[(n-2)(n-3).......1]}{2!(n-2)!}

     =  \frac{n(n-1)(n-2)!}{2!(n-2)!}

     = \frac{n(n-1)}{2!}

     = \frac{n(n-1)}{2}
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    \left( n \right)! = (n)(n - 1)\left[ {(n - 2)!} \right]
    Divide out (n-2)!.
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