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Question
Find n if nCn–2 = 15
Solution
nCn–2 = 15
∴ nC2 = 15 ...[∵ nCr = nCn–r]
∴ `("n"!)/(("n" - 2)!2!)` = 15
∴ `("n"("n" - 1)("n" - 2)!)/(("n" - 2)!2 xx 1)` = 15
∴ n(n – 1) = 30
∴ n(n – 1) = 6 × 5
Equating both sides, we get
∴ n = 6
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