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# Let n and k be any positive integers with k less than or equal to n. Prove C(n,k)=C(n,n-k).?

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- Iggy RockoLv 78 years agoFavorite Answer
C(n,n - k) =

n!/((n - k)! (n - (n - k))!) =

n!/((n - k)! (n - n + k)!) =

n!/((n - k)! k!) =

C(n,k)

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- ?Lv 68 years ago
C(n, k) = (n)! / [ (k)! (n -- k)! ] = (n)! / [ (n -- k)! (k)! ] = C(n, n -- k) QED

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