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Question
Find n, if `""^"n""C"_("n" - 2)` = 15
Solution
`""^"n""C"_("n" - 2)` = 15
∴ `("n"!)/(["n" - ("n" - 2)]!("n" - 2)!)` = 15
∴ `("n"!)/(2!("n" - 2)!)` = 15
∴ `("n"("n" - 1)("n" - 2)!)/(2 xx ("n" - 2)!)` = 15
∴ n(n – 1) = 15 × 2
∴ n(n – 1) = 30
∴ n(n – 1) = 6 × 5
∴ n = 6 ...(or n – 1 = 5)
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