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  1. #1
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    Show how...

    ... n(n-1 C r) = (r+1)(n C r+1)

    I can only get the left side n (n-1)! / r! (n-1-r)! = (r+1)(n C r+1)
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  2. #2
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    Quote Originally Posted by nafiro View Post
    ... n(n-1 C r) = (r+1)(n C r+1)

    I can only get the left side n (n-1)! / r! (n-1-r)! = (r+1)(n C r+1)
    LHS = n \frac{(n-1)!}{r! (n - 1 - r)!} = \frac{n (n-1)!}{r! (n - 1 - r)!}  = \frac{n!}{r! (n - r - 1)!}

    RHS = (r+1) \frac{n!}{(r + 1)! (n - [r+1])!} = \frac{(r+1) n!}{(r + 1)! (n - r - 1)!} = \frac{n!}{r! (n - r - 1)!} = LHS.
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