IIT JEE , AIEEE Forum - Mathematics , Algebra

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no of books: 0 1 2 .......... n

total selections:²ⁿ⁺¹C₀²ⁿ⁺¹C₁²ⁿ⁺¹C_{2 ..............}²ⁿ⁺¹C_n

(1+1)²ⁿ⁺¹=²ⁿ⁺¹C₀+²ⁿ⁺¹C₁+ ²ⁿ⁺¹C₂.............. +²ⁿ⁺¹C_n+.............²ⁿ⁺¹C_2n+1

2²ⁿ⁺¹=2(²ⁿ⁺¹C₀+²ⁿ⁺¹C₁+ ²ⁿ⁺¹C₂.............. +²ⁿ⁺¹C_n)

2²ⁿ=²ⁿ⁺¹C₀+²ⁿ⁺¹C₁+ ²ⁿ⁺¹C₂.............. +²ⁿ⁺¹C_{n ...........}(1)

given ²ⁿ⁺¹C₁+ ²ⁿ⁺¹C₂.............. +²ⁿ⁺¹C_n=63

Hence 2²ⁿ=1 +63 from (1)

Hence n=3

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