In this paper we demonstrate a simple computational procedure for the simulation of transport in a disordered semiconductor in which both multi-trapping and hopping processes are occurring simultaneously. We base the simulation on earlier work on hopping transport, which used a Monte-Carlo method. Using the same model concepts, we now employ a stochastic matrix approach to speed computation, and include also multi-trapping transitions between localised and extended states. We use the simulation to study the relative contributions of extended state conduction (with multi-trapping) and hopping conduction (via localised states) to transient photocurrents, for various distributions of localised gap states, and as a function of temperature. The implications of our findings for the interpretation of transient photocurrents are examined.