A five digit number is formed by using the digits 1, 2, 3, 4 and 5 without repetitions. What is the probability that the number is divisible by 4?

For a number to be divisible by 4, last 2 digits must be divisible by 4

Last 2 digits can be 12, 24, 32, 52

_, _, _, _, _

Last 2 digits have 4 possibilities and remaining digits can be arranged in 3! ways

Number of 5 digit numbers divisible by 4 are 3! $$\times\ $$ 4 = 24

Total number of 5 digit numbers that can be formed = 5!

Therefore, probability = $$\frac{24}{5!}\ $$ = $$\frac{1}{5}$$

Answer is option A.