2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/143121We give a probalistic proof of the famous Meinardus' asymptotic formula for the number of weighted partitions with weakened one of the three Meinardus' conditions, and extend the resulting version of the theorem to other two classis types of decomposable combinatorial structures, which are called assemblies and selections. The results obtained are based on combining Meinardus' analytical approach with probabilistic method of Khitchine.The version contains a few minor corrections.It will be published in Advances in Applied MathematicsProbabilityCombinatorics60C05;05A16;60F05text