  We consider a mixture of non-overlapping rods of different lengths $\ell_k$
moving in $\mathbb{R}$ or $\mathbb{Z}$. Our main result are necessary and
sufficient convergence criteria for the expansion of the pressure in terms of
the activities $z_k$ and the densities $\rho_k$. This provides an explicit
example against which to test known cluster expansion criteria, and illustrates
that for non-negative interactions, the virial expansion can converge in a
domain much larger than the activity expansion. In addition, we give explicit
formulas that generalize the well-known relation between non-overlapping rods
and labelled rooted trees. We also prove that for certain choices of the
activities, the system can undergo a condensation transition akin to that of
the zero-range process. The key tool is a fixed point equation for the
pressure.
