Discussion
The number of distinct ways in which 7 identical Fermions can be distributed in 3 energy levels is :
Answer: C
The number of ways is 0.
Identical fermions obey the Pauli exclusion principle: no two can occupy the same single-particle state. Three energy levels (each a single state) can hold at most three fermions, and even if each level held two of opposite spin, the limit would be six. Seven identical fermions therefore cannot be distributed in three levels at all.
The other numbers belong to other statistics: \(3^{7}\) counts distinguishable (Maxwell-Boltzmann) particles, and \(\frac{7!}{4!3!} = 35\) and 210 are combinatorial counts that ignore the exclusion principle.
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