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Question
If `""^(("n" – 1))"P"_3 : ""^"n""P"_4` = 1 : 10 find n
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Solution
Given `""^(("n" – 1))"P"_3 : ""^"n""P"_4` = 1 : 10
nPr =`("n"!)/(("n" - "r")!)`
`(("n" - 1)"P"_3)/(""^"n""P"_4) = 1/10`
`((("n" - 1)!)/(("n" - 1 - 3)!))/(("n"!)/(("n" - 4)!)) = 1/10`
`(("n" - 1)!)/(("n" - 4)!) xx (("n" - 4)!)/("n"!) = 1/10`
`(("n" - 1)!)/("n"!) = 1/10`
`(("n" - 1)!)/("n"("n" - 1)!)= 1/10`
`1/"n" = 1/10`
⇒ n = 10
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