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We introduce the general method of converting a given operator function into its s-ordered form. We state and prove a theorem representing the fact that any ordered expansion of some operator function might be considered as the combinatorial problem of counting the number of contractions. This will also unify the two essentially distinct notions of'taking an operator into some ordered form'and'reordering, or formally, ordering an operator'. In this way, we reduce the general ordering problem into a purely combinatorial one. Finally, we show the application of the theorem through two generic examples from both quantum optics and field theory.