A 5-digit number divisible by 3 is to be formed using the number 0,1,2,3,4 and 5 without repetiition. Find total of ways in whiich this can be done.

Explanation

A number is divisible by 3 when the sum of the digits of the number is divisible by 3.

Out of the given 6 digits, there are only two groups consisting of 5 digits whose sum is divisible by 3.

`1 +2+3 + 4 + 5 = 15`

`0+ 1 + 2 + 4 + 5 = 12`

Using the digits `1, 2, 3, 4 ` and `5`, and 5 digit numbers that can be formed `= 5!`

Similarly, using the digits `0, 1, 2, 4` and `5`, the number that can be formed `= 5! - 4! `(since the first digit cannot be 0)

∴Total numbers that are possible `5! + 5! - 4! = 240 - 24 = 216`