The method of cumulants expansion for both averaged singleparticle and two-par-ticle Green's functions for a disordered binary alloy is extended to treat a disordered n-component alloy. Within the single-site approximation, if the multipleoccupancy cor-rections are treated self-consistently, it is shown that both averaged single-particle and two-particle Green's function agree with the results of coherent potential approximation.