Wednesday, October 11, 2017

discrete mathematics - Proof using double counting


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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