Question

A $4-$ digit number is formed by the digits $0,1,2,5$ and $8$ without repetition. Find the probability that the number is divisible by $5$.

Answer 1

Total possibility $=5!$

Favorable outcomes $=2\times 4!$ (to be divisible by $5$ unit digit can be filled with only $0$ or $5$, so only two possibilities are there, then the remaining can be filled in $4,3$ and $2$ ways respectively)

So probability $=\frac{2\times 4!}{5!}=\frac{2\times 4!}{5\times 4!}=\frac{2}{5}$