Question

The number of $n$ digit numbers which consists of the digits $1$ and $2$ only if each digit is to be used atleast once is equal to $510$ then $n$ is equal to

• A. $7$
• B. $8$
• C. $9$
• D. $10$

Answer 1

Answer: (C)

$9$

Number with atleast one occurrence $=$ total number of occurrence of $1-$ occurrence of $2$.

$510=(2\times 2\times \mathrm{2....}\times 2)ntimes-2$

$\Rightarrow 510=2^n-2$

$\Rightarrow 2^n=512$

$\Rightarrow 2^n=2^9$

$\therefore n=9$