In how many ways can five-digit numbers be formed by using digits $0,2,4,6,8$ such that the numbers are divisible by $8$?
Assume the case in which repetition is not allowed
Case1: When repetition is not allowed.
We start to make pairs of combinations such that they are divisible by $8$ and left over number can be selected in the following ways also.
Is there any other approach (without making cases as it can be too long) through which I can solve this problem?