Q. An $n$-digit number is a positive number with exactly $n$ digits. 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
Explanation
(b)
The number of distinct $n$-digit numbers to be formed using digits 2, 5 and 7 is $3^{n}$. We have to find $n$ so that
$3^{n} \geq 900 \Rightarrow 3^{n - 2} \geq 100$
$\Rightarrow \ n - 2 \geq 5 \Rightarrow n \geq 7$
So the least value of $n$ is 7
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.