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Question
Find n if nCn–3 = 84
Solution
nCn–3 = 84
∴ `("n"!)/(("n" - 3)!["n" - ("n" - 3)]!)` = 84
∴ `("n"("n" - 1)("n" - 2)("n" - 3)!)/(("n" - 3)! xx 3!)` = 84
∴ n(n – 1)(n – 2) = 84 × 6
∴ n(n – 1)(n – 2) = 9 × 8 × 7
Comparing on both sides, we get n = 9
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