  We 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.
