Question

The number of $n$ digit numbers which consists of the digits $1$ & $2$ 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)

$9$

Basically we have $n$ blank spaces in which we have to put $1$ and $2$

$\therefore$ Total such occurance $=2^n$

But we have to subtract the cases where there is no occurance of $1$ and no occurance of $2$

Hence, Number with atleast one occurance

$=2^n-1-1=2^n-2$

$2^n-2=510$ $\Rightarrow n=9$

Hence correct answer is $9$