Question

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 at least one book is 255, then n is

• A. 3
• B. 4
• C. 5
• D. 8

Answer 1

Answer: (B)

4

Answer 2

$2n + 1C_{1} +^{2n + 1}C_{2} + ... +^{2n + 1}C_{n} = 255$

⇒ $2n + 1C_{0} +^{2n + 1}C_{1} + ... +^{2n + 1}C_{n} = 256$

⇒ $\frac{2^{2n + 1}}{2} = 256 \Rightarrow n = 4$