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Algebra

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5 Feb 2012 18:08:00 IST

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Combination

Mathematics

A student is allowed to select at most n books from a collection of (2n+1) books. If the total number of ways in which he can select a book is 63 . Find the value of n .

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Vishal U. Karve

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Joined: 18 Jan 2012

Posts: 147

5 Feb 2012 18:42:23 IST

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²ⁿ⁺¹C₁+²ⁿ⁺¹C₂+...+²ⁿ⁺¹C_n is the required no. of ways.

Simplifying...

=1/2 [²ⁿ⁺¹C₁+²ⁿ⁺¹C₂+...+²ⁿ⁺¹C_2n]

=1/2[2²ⁿ⁺¹-2]

=2²ⁿ-1

Given,

2²ⁿ-1=63

2²ⁿ=64

2²ⁿ=2⁶

n=3

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