Question

In a library there are $(2n+1)$ books. If a student selects atleast $(n+1)$ books in $256$ ways, then the number of books in the library is

• A. $7$
• B. $8$
• C. $9$
• D. $6$

Answer 1

The correct option is B $8$

Since the student is allowed to select atleast $(n+1)$ books out of $(2n+1)$ books, the total number of ways of selecting is

${}^{2n+1}{C}_{n+1}{+}^{2n+1}{C}_{n+2}{+}^{2n+1}{C}_{n+3}+......{+}^{2n+1}{C}_{2n+1}=256$

$2^{2n+1}=256$

$2^{2n+1}=2^8$

$\therefore 2n+1=8$