A five digit number divisible by 6 is to be formed by using the digits 0, 1, 2, 3, 4 and 8 without repetition. The total number of ways in which this can be done is

Since 0 + 1 + 2 + 3 + 4 + 8 = 18, the 5 digit number will be divisible by 3 if either 0 or 3 is not used. When 0 is not used. For the unit place we have 3 choices (2, 4 or 8) and for the remaining place we have 4! Choices.When 3 is not used  In this case, 0 is used at the unit’s place, the number of choices is 4! If 0 is not used at the unit’s place, then unit’s place can be filled up in 3 ways and the remaining places in (4! – 3!) ways. Thus, required number of numbers=3(4!)+4!+3(4!−3!)=150