2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/108827We give simple necessary and sufficient conditions for the inclusion-exclusion identity to hold for an infinite countable number of sets. In terms of a random variable, whose range are nonnegative integers, this condition is equivalent to the convergence to zero of binomial moments. Some standard extensions of the countable inclusion-exclusion identity are also given.4 pagesProbabilityCombinatorics05A19, 05A20, 60C05text