IIT-JEE 1998Question 1
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
Permutation and Combination
Solution
Concept. Each of the $n$ places has $3$ choices: $3^n$ numbers. Formulas used. (1) Multiplication principleStep 1 - Need. $3^n\ge900$. Step 2 - Powers. $3^6=729<900$, $3^7=2187\ge900$. Step 3 - Smallest. $n=7$. Answer: B