Question

In a library there are $n$ different books on mathematics, and one can draw any number of books. If the number of ways in which the books can be drawn is $4095$, then ?

• A. $n=9$
• B. $n=10$
• C. $n=11$
• D. $n=12$

Answer 1

The correct option is D $n=12$

${}^n{C}_1{+}^n{C}_2{+}^n{C}_3+...{.}^n{C}_n=4095$

$\Rightarrow 2^n-1=4095$

$2^n=4096$

$\Rightarrow n=12$