Question

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

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{4}$
• D. $\frac{1}{5}$

Answer 1

The correct option is D $\frac{1}{5}$

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

A number divisible by $4$ formed using the digits $1,2,3,4$ and $5$ has to 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. Total number of numbers divisible by $4$ can be formed in $6\times 4=24$ ways.

Required probability:

$P=\frac{24}{120}=\frac{1}{5}$