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**1. Homework Statement**

In the canonical ensemble, the probability that a system is in state r is given by

[tex] P_i = \frac{g_i \exp (-\beta E_i)}{\sum_i g_i \exp( -\beta E_i)} [/tex]

where g_i is the multiplicity of state i. This is confusing me because I thought

[tex] P_i = \frac{g_i}{\sum_i g_i} = [/tex] states consistent with i / total number of states

was always true by the equal probabilities postulate. What am I missing? Are those two expressions the same?

**2. Homework Equations**

**3. The Attempt at a Solution**