Question

The number of numbers between $2,000$ and $5,000$ that can be formed with the digits $0,1,2,3,4$ (repetition of digits is not allowed) and are multiple of 3 is:

Answer 1

Number between $2000$ & $5000$ is a four digit number.

Possible set of $4$ digits that have sum divisible by $3$

$0,1,2,3,\to$ set I

$0,2,3,4\to$ set II

For set-I First digit can be $2$ or $3$ only as number should be between $2000$ to $5000$

$\overline{2}$ $\overline{3}$ $2$ $\overline{1}$

$2\times 3\times 2\times 1=12$ ways

For set-II First digit can be $2,3$ or $4$

$\overline{3}$ $\overline{3}$ $\overline{2}$ $\overline{1}$

$3\times 3\times 2\times 1=18$ ways

$12+18=30$ numbers can be formed.