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We show how the multi-step direct reaction series can be evaluated using Monte Carlo methods. Nucleon-nucleon collisions occur according to the random selection of a nucleon’s attenuation factor along its classical trajectory. The particles and hole excited in a collision are selected from a local Fermi distribution. We assume that the particles continue to propagate and possibly collide again before leaving the nucleus. We assume that holes collide in place, to possibly produce other particles and holes.