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Counting the Ways

If we accept the FUNDAMENTAL ASSUMPTION at face value, then it is easy to calculate the probability of finding the equilibrated system in any given fully specified state: if the state is not accessible [e.g. if it takes more energy  U  than we have at our disposal] then the probability is zero; if it is accessible, then its probability is just   ${1 \over \Omega}$,  where  $\Omega$  is the total number of accessible states. The first step is therefore to calculate  $\Omega$. In general this can get difficult, but we can choose a few simple examples to illustrate how the calculation goes.