Question

$n$-digit numbers are formed using only three digits $2,5$ and $7$. The smallest value of $n$ for which $900$ such distinct numbers can be formed, is :

• A. $6$
• B. $7$
• C. $8$
• D. $9$

Answer 1

The correct option is B $7$

With repetition the total $n$ digits number that can be formed using $2,5$ and $7.$
So total distinct numbers possible $=3^n$
Then the smallest value of $n$ for which $900$ such distinct numbers can be formed will be
$3^n>900\Rightarrow 3^{n-2}>100$
So the minimum $n$ will be,
$n-2=5\Rightarrow n=7$