  We find the distribution of transmission eigenvalues in a series of identical
junctions between chaotic cavities using the circuit theory of mesoscopic
transport. This distribution rapidly approaches the diffusive wire limit as the
number of junctions increases, independent of the specific scattering
properties of a single junction. The cumulant generating function and the first
three cumulants of the charge transfer through the system are obtained both in
the normal and in the superconducting state.
