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i am supposed to show that

Sigma of k = 0 to m, (n, k) (n - k, m - k) = 2^m (n, m)

So I have after expanding:

(n, k) = n!/(n-k)!k! and (n-k, m-k) = (n-k)!/(m-k)!(n-m)!

so together the (n-k)! cancels out and I have

n!/k!(m-k)!(n-m)!

and that is

n!/m!(n-m)! which is

(n, m)

so then I can take (n, m) out of the sigma and then I would have

(n, m)*Sigma from k = 0 to m 1, but then how do I get the 2^m?

Thanks.