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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

Option: 1

216


Option: 2

150


Option: 3

116


Option: 4

98


Answers (1)

best_answer

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, if 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

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