Question

An n-digit number is a positive number with exactly n digits. Atleast nine hundred distinct n-digit numbers are to be formed using only the three 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

The correct option is B

7

Since at any place, any of the digits 2, 5 and 7 can be used, total number of such positive n-digit numbers are $3^n$. Since, we have to form atleast 900 distinct numbers, $3^n\ge 900\Rightarrow n\ge 7$.

Therefore, the smallest value of n is 7.