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Question
Find n if n – 1P3 : nP4 = 1 : 9
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Solution
n – 1P3 : nP4 = 1 : 9
`=> (""^("n" - 1)"P"_3)/(""^"n""P"_4) = 1/9`
⇒ `[ ((n - 1)!)/((n - 1 - 3)!)]/[(n!)/((n - 4)!)] = 1/9`
⇒ `((n - 1)!)/((n - 4)!) xx ((n - 4)!)/(n!) = 1/9`
⇒ `((n - 1)!)/(n xx (n - 1)!) = 1/9`
⇒ `1/n = 1/9`
∴ n = 9
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