Question

Find the number of four digit numbers that are less than $2000$ that can be formed with the digits $1,2,3,4$ such that each digit can be repeated any number of times

• A. $24$
• B. $25$
• C. $64$
• D. $65$

Answer 1

The correct option is C $64$

Given that the numbers should be less than $2000$, so the first digit can only be filled by $1$
The other three digits can take any of the four given values in 4 ways each
$\therefore$ Required number of $4$-digit numbers $=1\times 4^3=64$