Question

The number of $5$ digit numbers which are divisible by $4$, with digits from the set $\{1,2,3,4,5\}$ and the repetition of digits is allowed, is ________?

Answer 1

A number is divisible by $4$ if last two digits of that number is divisible by $4$

The $2$ digits numbers which are divisible by $4$ from the given set $\{1,2,3,4,5\}$ are $12,24,32,44$ or $52$

So, if a number ends with $12,24,32,44$ or $52$, then it is divisible by $4$

First $3$ digits can be arranged in $5^3$ ways

So, the total number of $5$ digit numbers which are divisible by $4$ without repetition is

$5^3\times 5=625$