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4. Returning to our 3-D particle in a box with equal sides, states with different indices are distinct even though the energies are degenerate; that is, for example
\[ \psi_{1,1,2} (x, y, x) \neq \psi_{1,2,1} (x, y, x) \neq \psi_{2,1,1} (x, y, x) \]

Given this fact,

(a) How many total spin-\(\frac{1}{2}\) fermions can I pack in the first 3 energy levels?

(b) How does this answer change for spin-\(\frac{3}{2}\) fermions?

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