Let $B$ be a finite set in $\mathbf{P}^1(\mathbf{C})$. Let $G$ be the fundamental group of $\mathbf{P}^1(\mathbf{C}) - B$.
We can view $G$ as a subgroup of $\mathrm{SL}_2(\mathbf{R})$.
Why is $G$ Fuchsian of finite volume?
That is, why is $G$ a discrete subgroup of finite volume?