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Question
Find n if `""^"n""C"_("n" - 3)` = 84
Solution
`""^"n""C"_("n" - 3)` = 84
∴ `("n"!)/(("n"-3)!["n"-("n"-3)]!)` = 84
∴ `("n"("n" - 1)("n" - 2)("n" - 3)!)/(("n" - 3)!xx3!` = 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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