Question

A five digit number is formed with the digits 0, 1, 2, 3 and 4 without repetition. Find the chance that the number is divisible by 5.

• A. $\frac{3}{5}$
• B. $\frac{1}{5}$
• C. $\frac{2}{5}$
• D. $\frac{4}{5}$
• E. None of these

Answer 1

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

Since, $0$ will not be included at the ten thousand place.
$5$ digit number $=4\times 4!$

Divisible by $5$ then the last digit should be $0$
Then the remaining position have the possibility $=4!$
Therefore, the required probability, $P=\left(\frac{4!}{4\times 4!}\right)=\frac{1}{4}$