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Math Help - Combinations simplification, please revise and help

  1. #1
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    Combinations simplification, please revise and help

    Hi, I'm trying to simplify this but I get stuck at some point.

    it goes 1/n! * C(n,2) * P(n,n-2)

    which yields:

    1/n! * n!/2!(n-2)! * n!/(n - (n-2))!

    which so far I have reduced down to

    2! * (n-2)! * n! / (n - (n - 2))!

    Is this correct? help with further simplification? Thank you!
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  2. #2
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    Quote Originally Posted by domain07 View Post
    Hi, I'm trying to simplify this but I get stuck at some point.

    it goes 1/n! * C(n,2) * P(n,n-2)

    which yields:

    1/n! * n!/2!(n-2)! * n!/(n - (n-2))!

    which so far I have reduced down to

    2! * (n-2)! * n! / (n - (n - 2))!

    Is this correct? help with further simplification? Thank you!
    Hmm, I get

    P(n,n-2)=\frac{n!}{(n-(n-2))!}

    P(n,n-2)=\frac{n!}{2}

    and C(n,2)=\frac{n!}{(n-2)!\cdot2!}

    Overall, \left(\frac{1}{n!}\right)\cdot C(n,2)\cdot P(n,n-2)

    =\left(\frac{1}{n!}\right)\left(\frac{n!}{2}\right  )\left(\frac{n!}{(n-2)!\cdot2!}\right)

    =\frac{n!}{(n-2)!\cdot4}

    =\frac{n\cdot(n-1)\cdot(n-2)!}{(n-2)!\cdot4}

    =\frac{n(n-1)}{4}
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