A five-digit number is formed by the digit 1, 2, 3, 4, 5 without repetition. Find the probability that the number formed is divisible by 4.

Answer

`(1)/(5)`

Explanation

Total number of numbers formed by the digits 1, 2, 3, 4, 5 without repetition is `5! = 120`. Now we know that a number is divisible by 4 if the number placed at its last two digits is divisible by 4. So that last two digits can be 12, 24, 32 or 52, i.e., they can be filled in 4 ways. There are `3! = 6` ways of filling the other three places.
Therefore, the favorable numberof ways is `4 xx 6` = 24 ltbgt Hence, the required probability is
`P = ("Favorable no. of cases")/("Exhaustive no. of cases")=(24)/(120) = (1)/(5)`