Answer to Question #257890 in Discrete Mathematics for suehaiza

Question #257890

prove that n.P(n-1,n-1)=p(n,n)

Expert's answer

Solution:

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

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