Question

A five digit number is formed by the digits 1, 2, 3, 4, 5 without repetition. Find the probability that the number is divisible by 4.

Answer 1

A number divisible by $4$ formed using the digits $1,2,3,4$ and $5$ should have the last two digits $12$ or $24$ or $32$ or $52$.

In each of these cases, the five digits number can be formed using the remaining $3$ digits in $3!=6$ ways.

A number divisible by $4$ can be formed in $6\times 4=24$ ways

Total number of 5-digit numbers that can be formed using the digits $1,2,3,4$ and $5$ without repetition $=5!=120$

Required probability $=\frac{24}{120}=\frac{1}{5}$