Question

Nine hundred 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. 6
• B. 7
• C. 8
• D. 9

Answer 1

Answer: (B)

7

Given digits are $2,5$ and $7$.
An $n$-digit number is to be formed using these digits.
Out of $n$ places, each place can be filled in $3$ ways. So, total number of ways $=3^n$ .
Now, $3^n\ge 900$
$3^n\ge 3^{2}100$
$\Rightarrow n-2\ge 5$
So,least value of $n$ is $7$.