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

Let us observe the digits given to us, we have 0,1,2,3,4 and 5, to make a five digit number we only need 5 digits out of the given 6 digits,
Case 1: Using digits 0,1,2,4 and 5.
The number of ways in which we can arrange these 5 digits are ⇒4×4×3×2×1
⇒96
Case 2: Using the digits 1,2,3,4 and 5
The number of ways in which we can arrange these 5 digits are ⇒5×4×3×2×1
⇒120
Therefore, the total number of cases =96+120=216