How to count all ways to arrange Bosons?

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The discussion highlights a critical error in calculating the arrangement of bosons by incorrectly applying methods meant for distinguishable particles. It emphasizes that the enumeration of states must account for the indistinguishable nature of identical bosons. Participants argue that the correct approach requires a different combinatorial method to accurately reflect bosonic behavior. The conversation underscores the importance of recognizing the unique properties of bosons in statistical mechanics. Accurate counting of arrangements is essential for understanding quantum statistics.
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Homework Statement
This is very basic question but to be honest I dont understand even though I read Pointon's book. The question said what is all possible ways to arrange Bosons and how much is the total configuration. The energy states/levels are = 1E, 2E, and 3E. The total of boson particles are 2, and all of the states should have degeneracy/g_j = 3 and total Energy E = 4.

Is my answer incorrect? Thank you
Relevant Equations
W = \frac{(n+g-1)!}{n!(g-1)!}
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In your enumeration of states, you are missing one case.

Your calculation on the right is correct only for distinguishable particles. This should not apply to identical bosons.
 

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