Using covering spaces, prove that for each integer $n \geq 2$, $F_n$ is a finite index subgroup of $F_2$, where $F_n$ is the free group on $n$ generators.
I get how the cayley graph of $F_n$ would be a wedge of $k$ circles and the cayley graph of $F_2$ would be a graph of a vertex and two edges, but I don't understand how we can create an injective map from $F_n$ to $F_2$ and show its a subgroup.
Hint: the fundamental group of a space which looks like $$\underbrace{\bigcirc\!\!\bigcirc\cdots \bigcirc\!\!\bigcirc}_{n\mbox{ circles}}$$
is $\pi_1= F_n$. Can you think of a covering map from this space onto the wedge of two circles? (try with three circles first).