Question

The number of numbers between $2000$ and $5000$ that can be formed with the digits $0,1,2,3,4$ (repetition of digits is not allowed) and are multiple of $3$ is :

• A. $36$
• B. $30$
• C. $24$
• D. $48$

Answer 1

The correct option is B $30$

Since, the numbers are multiple of $3,$ then the sum of digits must be divisble by $3.$
Hence, possible combinations are: $(0,1,2,3)\&(0,2,3,4)$
$\therefore$ Numbers of $4$ digits numbers that lie between $2000$ and $5000$ is $2\times 3!+3\times 3!=30$