A multigroup, collision-probability, order-of-scattering approach is made to the slowing down solution of the neutron transport equation in a heterogeneous, non-multiplying medium with sources. Introducing first-collision probabilities in the Liouville-Neumann series solution of the neutron flux, the series may be summed and a transport matrix defined. If a flat source distribution in the region is assumed, this matrix is typical of the medium and of the geometrical configuration only and links, in an explicit way, sources and resultant fluxes. In a multiplying system without external sources it is also possible to use the above transport model when determining the effective neutron multiplication factor by the fission probability matrix method.