Q.
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