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 :

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 : (A) 24 (B) 30 (C) 36 (D) 48

Tardigrade Admin · Accepted Answer

Number between 2,000 and 5,000 is 4 digits number.
Using

0, 1, 2, 3, 4

(repetition of digits is not allowed) and are multiple of 3 .
For multiple of 3 , the sum of all digits should be divisible by

3

So, number can be formed

0, 1, 2, 3

(sum is 6 which is divisible by 3) or

0, 2, 3, 4

(sum is 9 which is divisible 1 cannot be on highest digit in the number.
Therefore, number of 4 digit numbers

= 2 \times 3! + 3 \times 3! = 30

Q. 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 :

24

30

36

48

Q. 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 :