  We give the asymptotic growth of the number of (multi-)arcs of bounded length
between boundary components on complete finite-area hyperbolic surfaces with
boundary. Specifically, if $S$ has genus $g$, $n$ boundary components and $p$
punctures, then the number of orthogeodesic arcs in each pure mapping class
group orbit of length at most $L$ is asymptotic to $L^{6g-6+2(n+p)}$ times a
constant. We prove an analogous result for arcs between cusps, where we define
the length of such an arc to be the length of the sub-arc obtained by removing
certain cuspidal regions from the surface.
