A new method to construct a formula for the entropy of mixture systems is suggested. Using the exact values of the entropy at high and low temperature boundaries, an approximate formula of the entropy in the entire range can be obtained. This method is applied to the A, B mixture on square lattices as a first example and then extended to the A-A, B (dimer monomer) mixture system. This method is a ''macroscopic'' way of derivation. Therefore it is free from the difficulties of counting the number of configurations in which all dimers must avoid each other. With non-zero coupling energies between monomers and dimers in a A-A, B mixture, our results indicates a unique phenomenon that in some narrow range of chemical potential, decreasing temperature will make more dimers stay in lattice but further decreasing will reverse the tendency and more monomers will occupy the lattice. This phenomenon is confirmed by our Monte Carlo simulations and can be easily explained by the closed formula.
