Computation of the probability distribution of electrons at the output of a photomultiplier is carried out by numerical integration along a contour in the complex plane, a method that is efficient even when the number of electrons is large. When the overall gain of the photomultiplier is fixed and the number of dynodes is increased, the single-stage secondary distribution being assumed the same for each, the output distribution approaches an exponential form for a broad class of single-stage distributions.