Question

A four digit number is formed using the digits 1, 2, 3, 5 with no repetitions. Write the probability that the number is divisible by 5.

Answer 1

$$\begin{gathered} \text{To be divisible by 5 ones place sholud be}5 \\ \text{There are 3 places remaining which can be filled in}3!=6\text{ways} \\ \mathrm{So},6\text{numbers can be formed out of 1, 2, 3 and 5, which are divisible by}5. \\ \text{Total 4-digit numbers}=4!=24 \\ P\left(\text{4-digit number divisible by}5\right)=\frac{6}{24} \\ =\frac{1}{4} \end{gathered}$$