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