The Short and Long Range Orders in alloys can be considered based on a new expression for the combinatorial factor. This expression is more convenient and intuitive than the traditionally used form and can be directly applied to reproduce the results of several good known statistical-thermodynamic models that usually are considered completely independent or even inconsistent.The short list includes quasichemical theory, associated solution model, surrounded atom model, cluster site approximation.As result, the formalism and interpretation of these models are significantly clarified, allowing simultaneously to identify and fix several long standing errors that otherwise could be left unnoticed.Multicomponent generalization of listed models is also critically simplified.For the systems experiencing a phase transition, the advanced version of theory provides a mechanism allowing to reproduce the correct critical temperature of conversion and at the same time to increase significantly the precision of thermodynamic functions.