knight247 wrote:Of all the five-digit integers formed by permutation of the digits 1, 2, 3, 4 and 5 without repition. what is the probability that a five-digit integer drawn randomly will be divisible by 4
(A) 1/10
(B )4/15
(C) 13/30
(D) 1/5
(E) 3/20
Hope i can get a detailed explanation on this one. OA is D
Total no. of ways of arranging 5-digit integers without repetition = 5! = 5 * 4 * 3 * 2 * 1 = 120
An integer is divisible by 4 if the last 2 digits are divisible by 4.
In this case, the possibilities of a 5-digit integer divisible by 4 can be the following:
_ _ _ 12, where 3 blank spaces can be filled by any of the numbers 3, 4, and 5. So, this can be done in 3! = 6 ways
_ _ _ 32, where 3 blank spaces can be filled by any of the numbers 1, 4, and 5. So, this can be done in 3! = 6 ways
_ _ _ 42, where 3 blank spaces can be filled by any of the numbers 1, 3, and 5. So, this can be done in 3! = 6 ways
_ _ _ 52, where 3 blank spaces can be filled by any of the numbers 1, 3, and 4. So, this can be done in 3! = 6 ways
So, the possible 5-digit integers that are divisible by 4 and none of the digits repeat = 6 * 4 = 24
Hence, the required probability = 24/120 = [spoiler]1/5[/spoiler]
The correct answer is D.
