Equivalent expression to nPn-1?

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Answer 1 · 2018-06-06T15:15:37

$\frac{n!}{(n - 1)!} or n$ $(n!)/((n - 1)!) or n$

$^{n} P_{n - 1}$ $"^nP_(n-1)$

Recall;

$^{n} P_{r} = \frac{n!}{(n - r)! r!}$ $"^nP_r = (n!)/((n - r)!r!)$

Therefore;

$^{n} P_{n - 1} = \frac{n!}{(n - (n - 1)) (n - 1)!}$ $"^nP_(n-1) = (n!)/((n - (n - 1))(n - 1)!)$

$^{n} P_{n - 1} = \frac{n!}{(n - n + 1) (n - 1)!}$ $"^nP_(n-1) = (n!)/((n - n + 1)(n - 1)!)$

$^{n} P_{n - 1} = \frac{n!}{1 (n - 1)!}$ $"^nP_(n-1) = (n!)/(1(n - 1)!)$

$^{n} P_{n - 1} = \frac{n!}{(n - 1)!}$ $"^nP_(n-1) = (n!)/((n - 1)!)$

Can also be further simplified to;

$^{n} P_{n - 1} = \frac{n \times (n - 1)!}{(n - 1)!}$ $"^nP_(n-1) = (n xx (n - 1)!)/((n - 1)!)$

$"^nP_(n-1) = (n xx cancel((n - 1)!))/cancel((n - 1)!)$

$"^nP_(n-1) = n$