Give two proofs that (2n)!=(2nn)⋅(n!)2
I've already determined how to prove it algebraically (I think):
(2nn)=(2n)!(n!)2
(2n)!=(2n)!(n!)2∗(n!)2
(2n)!=(2n)!
But how would you go about proving it through double counting? Any pointers on how to formulate the proof would be appreciated, thanks.
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