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

A five-digit number, which is divisible by 3, is formed when sum of digits is also divisible by 3.
So, combination formed using six-digits, which are divisible by 3
= 5 + 4 + 3 + 2 + 1 = 15
= 5 + 4 + 2 + 1 + 0 = 12
So, set of number are (5, 4, 3, 2, 1) and (5, 4, 2, 1, 0).
Number formed by using 1st set = 5 x 4 x 3 x 2 x 1 = 120
Similarly, using 2nd set = 4 x 4 x 3 x 2 x 1 = 96
Hence, using 2nd set, underlined place cannot be filled by 0, otherwise it will become a four-digit number.
∴ Total number = 120 + 96 = 216