Question

$900$ distinct n-digit positive numbers are to be formed using only the digits $2,5$ and $7$. The smallest value of $n$ for which this is possible, is

• A. $9$
• B. $8$
• C. $7$
• D. $6$

Answer 1

The correct option is C $7$

There are three ways to fill up each place. So, $n$ places can be filled in $3^n$ ways.
Therefore, total number of $n$ digit numbers $=3^n$
Now, $3^n\ge 900\Rightarrow n\ge 7$
Hence, the smallest value of $n$ is $7$.