A five digit number is formed by writing digits 1,2,3,4,5, in a random order without repetitions. Then, the probability that the number is divisible
by 4, is

The number is divisible by 4, if last two digits are 12, 24,32 and 52.
Remaining three place can be filled by 3! ways.
$\therefore$Favorable cases = 3! x4
Required probability $=\frac{3!\times 4}{5!}=\frac{3!\times 4}{5\times 4\times 3!}=\frac{1}{5}$