An n-digit number is a positive number with exactly `n` digit 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`

Options

A. 6
B. 7
C. 8
D. 9

Answer

B

Explanation

Distinct n - digit numbers which can be formed using digits 2, 5 and 7 are `3^(n)`. We have to find n, so that
`3^(n) ge 900`
`rArr" " 3^(n - 2) ge 100`
`rArr" " n - 2 ge 5`
`rArr" " n ge 7`, so the least value of n is 7.