A five digit number divisible by 3 is to be formed using the numerals 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways this can be done is

We know that a number is divisible by 3 if the sum of its digits is divisible by 3.Now the sum of the digits 1, 2, 3, 4 and 5 is 15, which is divisible by 3.∴ All the five digit numbers formed by the digits 1, 2, 3, 4, 5 are divisible by 3 and their number = 5! = 120.When we include 0, the four other digits whose sum is divisible by 3 are 1, 2, 4 and 5.∴ The number of numbers in this case =4×4!=4×24=96.Hence the required number of numbers = 120 + 96 = 216.