Aptitude | Probability | Question 8

A 5 digit number is formed by using digits 1, 2, 3, 4 and 5 with no two digits same. What is the probability that the formed number is divisible by 4?
(A) 1/5
(B) 4/5
(C) 3/5
(D) 1/4


Answer: (A)

Explanation: To be divisible by 4, the number has to end with the last two digits forming a number divisible by 4. Since there are only 5 digits: 1, 2, 3, 4, 5.
So, possible last two digits according to divisibility by 4:
12
24
32
52
For each of them we now have to put the remaining numbers in front: 3x2x1, therefore 6 combinations for each number set = 6×4 (we have 4 sets from above) = 24.

So, required probability is:

P = Number of desired outcomes / number of possible outcomes
= 24 /(5*4*3*2*1)
= 24 / (5!)
= 24 / 120
= 1/5

So, option (A) is correct.

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