The goal is to determine the multiplicity as a function of U ; from there, the entropy and other thermodynamic properties of the system can be determined. However, it is useful as an intermediate step to calculate multiplicity as a function of N ↑ ↑ and N ↓ ↓ . This approach shows that the number of available macrostates is N + 1. For example, in a very small system with N = 2 dipoles, there are three macrostates, corresponding to N ↑ ↑ = 0 , 1 , 2. Since the N ↑ ↑ = 0 and N ↑ ↑ = 2 macrostates require both dipoles to be either anti-aligned or aligned, respectively, the multiplicity of either of these states is 1. However, in the N ↑ ↑ = 1 , either dipole can be chosen for the aligned dipole, so the multiplicity is 2. In the general case, the multiplicity of a state, or the number of microstates, with N ↑ ↑ aligned dipoles follows from combinatorics, resulting in Ω Ω = N ! N ↑ ↑ ! ( N − − N ↑ ↑ ) ! = N ! N ↑ ↑ ! N ↓ ↓ ! , where the second step follows from the fact that N ↑ ↑ + N ↓ ↓ = N .