Hi, I was looking for a proof or explanation of this. From Schroeder's Thermal Physics, pg 56, explaining interacting systems in equilibrium. The example in the text is two 3-harmonic oscillators with a total of 6 units of energy. So one macrostate is where each has 3 units of energy. The individual multiplicity of each is 10, but the total multiplicity is 100 when considered together (10*10). The explanation is "because the systems are independent of each other." I know there is something from introductory combinatorics which explains this (which is why he went no further), but I myself don't know. Any help?