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Find n if 2nCr–1 = 2nCr+1 - Mathematics and Statistics

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Question

Find n if 2nCr–1 = 2nCr+1 

Sum
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Solution

2nCr–1 = 2nCr+1 

We know that if nCr = nCy, then x = y or x + y = n

∴ r – 1 + r + 1 = 2n   ...[∵ x = y is not possible]

∴ 2r = 2n

∴ r = n

∴ n = r.

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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. (iv) | Page 65

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