A five digit number is formed by the digits 1,2,3,4,5 without repetition.

Explanation

Let a 5-digit number of abcde.
it will be divisible by 4, if 2d+e is divisible by 4.
`implies underset("Even")(ubrace(2d+e))` divisible by 4 `therefore` e must be even.
`impliesunderset("Should be even")ubrace(2(d+(e)/(2)))` is divisible by 4
`{:("Then, "e=2","d=1","2","5),("and "e=4","d=2):}}` Total four cases
`therefore` Required number of `underset("Number of ways")("ways "=4xx3!=24)`
Filling abc after filling de.
Aliter A number of will be divisible by 4, if the last two digits of the number is divisible by 4, then for divisible by 4, last two digits 12 or 24 or 32 or 52.