For a finite group G, the probability of two elements of G that commute is the commutativity degree of G denoted by P (G). As a matter of fact, if C = {(a, b) ∈ G×G | ab = ba}, then P (G) = |C| |G|2 . In this paper, we are going to find few formulas for P (G) independent of |C|; for some AC-groups, and also in some special cases of finite minimal non-abelian groups. Moreover, the study will present implications for certain qualified finite groups
