Show how...

**nafiro** · October 13th 2009, 12:13 PM

... 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)

**mr fantastic** · October 13th 2009, 05:42 PM

Originally Posted by nafiro

... 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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