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

625

Explanation

A number is divisible by 4 if last 2 digit number is divisible by 4.
`therefore` Last two digit number divisible by 4 from (1, 2, 3, 4, 5) are 12, 24, 32, 44, 52
`therefore` The number of 5 digit number which are divisible by 4, from the digit (1, 2, 3, 4, 5) and digit is repeated is
`5 xx 5 xx 5 xx (5 xx 1) = 625`