Consider a collection of N non-interacting particles. Each particle can be in one of R states. Themicrocanonical

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Consider a collection of N non-interacting particles. Each particle can be in one of R states. Themicrocanonical ensemble assumption states that, left to itself, the system will visit all allowed microstates with equal probability. The allowed microstates correspond to all the different ways one can allocate the R states to the N particles under the given constraints. Let ni denote the number of particles in state i. If there were no constraints there would be a total of

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