Discussion
The number of distinct ways in which 4 particles can be distributed in 7 energy levels if (i) they are distinguishable and (ii) if they are indistinguishable bosons respectively is :
Answer: D
The answer is (i) \(7^{4}\) and (ii) 210.
For distinguishable particles each of the 4 particles can go into any of the 7 levels independently, giving \(7^{4} = 2401\) arrangements.
For indistinguishable bosons only the occupation numbers matter, and any number may share a level. The count is the number of ways to place 4 identical balls in 7 boxes:
\[ \binom{4 + 7 - 1}{4} = \binom{10}{4} = 210 \]
The option \(4^{7}\) reverses the roles of particles and levels. \(7!/(4!\,3!) = 35\) is the count for fermions, where no two particles may share a level.
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