Question

There are 15 buses running between two towns. In how many ways can a man go to one town and return by a different bus?

Answer 1

$n=15$ Buses $⟶$ $r=2$ Rows

we know

${}^n{P}_r=\frac{n!}{(n-r)!}{\Rightarrow }^{15}{P}_2=\frac{15!}{13!}\Rightarrow \frac{15\times 14\times 13!}{13!}\Rightarrow 15\times 14$

$\Rightarrow 210$ ways

Therefore there are $210$ possible ways