Question

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

Answer 1

We have, two option for each digit of a $n$ digit number

so, total $2^n$ numbers are possible

$1$ and $2$ should be used once, so we have to subtract the numbers which have all digits as$1$ and all digits as $2$

two such cases are possible, hence

$2^n-2=510$
$\Rightarrow 2^n=512$
$\Rightarrow n=9$