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Find n if nCn–2 = 15 - Mathematics and Statistics

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Question

Find n if nCn–2 = 15

Sum
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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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Properties of Combinations
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Chapter 3: Permutations and Combination - Exercise 3.6 [Page 65]

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Balbharati Mathematics and Statistics 2 (Arts and Science) [English] Standard 11 Maharashtra State Board
Chapter 3 Permutations and Combination
Exercise 3.6 | Q 16. (v) | Page 65

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