# Find n, if nCn-2 = 15 - Mathematics and Statistics

Sum

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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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 6 Permutations and Combinations
Exercise 6.7 | Q 5 | Page 90