In a train, five seats are vacant, the number of ways three passengers can sit, is

Given,

In a train, there are $5$ seats which are vacant. We have to find the number of ways in which $3$ passengers can sit in train.

In fact, we are simply permuting $3$ passengers in the given $5$ vacant seats by ${}^5{P}_3$.

So, the number of ways $3$ passengers can sit is ${}^5{P}_3$ , i.e.

$$\begin{gathered} \frac{5!}{\left(5-3\right)!}=\frac{5!}{2!} \\ =\frac{5\times 4\times 3\times 2\times 1}{2\times 1}=60 \end{gathered}$$

Hence, option $\left(4\right)$ is correct.