Prove that n•P(n−1,n−1)= P(n,n).

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$LHS=n.P(n-1,n-1) \\=n\times \dfrac{(n-1)!}{(n-1-n+1)!} \\=n\times \dfrac{(n-1)!}{(0)!} \\=n\times \dfrac{(n-1)!}{1} \\=n(n-1)! \\=n! \\=\dfrac{n!}{0!} \\=\dfrac{n!}{(n-n)!} \\=P(n,n) \\=RHS$

Hence, proved.

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Question ID: mtid-5-stid-8-sqid-1374-qpid-1112