A five digit number is formed without repetition of the digits $1,2,3,4,5$ in a random order. What will be the probability that the number is divisible by $4$?
I tried to solve and after a bit of calculations and observations, I came to know that the number will be divisible by $4$ if the last 2 digits of the number are $12, 24, 32$ or $52$. But it took me so much time to observe this trend.
So my answer is as follows:
Number of favorable cases $= 3! \times 4 = 24$
Number of exhaustive cases $ = 5! = 120$
So the probability $= 1/5$
My question is that, is there any other method of solving it quickly?