Question

How many 5-digit numbers divisible by 6 can be formed using digits 0, 2, 4, 5, 6, 8, if repetition not allowed.

Answer 1

Sum of digits is 0 + 2 + 4 + 5 + 6 + 8 = 25 

∴ the numbers can be formed with the digits 0, 2, 5, 6, 8 as their sum is a multiple of 3 provided unit’s place has an even number.

So it can be done in 4! + 3.3.3! = 78 ways.