Matrices & Systems · Medium problem

Four small airports $P, Q, R, S$ have direct flights $P$-$Q$, $P$-$R$, $Q$-$R$, $Q$-$S$ and $R$-$S$ (each flyable in either direction), and no others – in particular, no direct flight $P$-$S$. How many ways can a traveler fly from $P$ to $S$ with exactly one stop?