Question

A five digit number is formed by the digits $1,2,3,4,5$ with no digit being repeated. The probability that the number is divisible by $4$, is

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

Answer 1

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

The number is divisible by $4$ only when it ends with:

$12,$ , $24,$, $32,$ or $52$

The number of possibilities in each of these cases is $3!$ as the digits at one's and ten's places are fixed and the rest $3$ digits can be chosen in $3!$ ways.

Thus total possibilities for digit to be divisible by $4=4\times 3!$

$P=\frac{\text{Numbers divisible by}4}{\text{Total numbers}}=\frac{4\times 3!}{5!}=\frac{1}{5}$