Question

If the total number of selections of at least (n + 1) things from $(2n+1)$ different things is 256, then the value of n is

• A. 2
• B. 3
• C. 4
• D. 8

Answer 1

Answer: (C)

${}^{(2n+1)}{C}_{(n+1)}+{}^{(2n+1)}{C}_{(n+2)}+\dots \dots ..+{}^{(2n+1)}{C}_{(2n+1)}=256$
$\frac{1}{2}\left[{}^{(2n+1)}{C}_0+{}^{(2n+1)}{C}_1+\dots \dots .+{}^{(2n+1)}{C}_{(2n+1)}\right]=256$
$\frac{1}{2}\cdot 2^{2n+1}=256\Rightarrow 2^{2n}=256=2^8\Rightarrow n=4$