Equivalent expression to nPn-1?

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Answer 1 · 2018-06-06T15:15:37

#(n!)/((n - 1)!) or n#

#"^nP_(n-1)#

Recall;

#"^nP_r = (n!)/((n - r)!r!)#

Therefore;

#"^nP_(n-1) = (n!)/((n - (n - 1))(n - 1)!)#

#"^nP_(n-1) = (n!)/((n - n + 1)(n - 1)!)#

#"^nP_(n-1) = (n!)/(1(n - 1)!)#

#"^nP_(n-1) = (n!)/((n - 1)!)#

Can also be further simplified to;

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

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

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