A cube can be envisioned as an assembly of identical octants (numbered 1-8 in no particular order).

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A cube can be envisioned as an assembly of identical octants (numbered 1-8 in no particular order). The cube contains three identical particles. How many basic states in this system yield a macrostate \((a)\) in which all three particles are in octant 1 and \((b)\) in which two particles are in octant 8 ?

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