Let G be a finite group. The commutativity degree of G denoted by P(G) is the probability of two group elements that commute. As a matter of fact, if C = {(x, y) ∈ G × G | xy = yx}, 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.
