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Counting Microstates of Fermions and Bosons

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Please explain to me how to solve the following two questions.(Explanations wills be highly appreciated)
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1. Count the number of physically different microstates for a system of n indistinguishable fermions, where each particle can be in k different non-degenerate eigenstates.

2. Count the number of physically different microstates for a system of n indistinguishable bosons, where each particle can be in k different non-degenerate eigenstates.

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Solution Summary

In this solution, we count the number of microstates of a system of fermions as well as a system of bosons.

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1. Fermions obey the Pauli exclusion principle, which says that no two can be in the same eigenstate. Thus the answer is zero unless k >= n, in which case there are k choices for the first fermion, k-1 for the second, etc., down to k-n+1 for the last fermion. Since the fermions are indistinguishable, the order of the fermions ...

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