The number of partitions of 4 with at most 3 parts is 3? Let's list:
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- Is (1,3,0) different? No.
- So only three distinct multisets.
- But standard stars and bars for unordered non-negative integers: number of integer partitions of 4 into at most 3 parts, where order doesn't matter, or equivalently, number of solutions in non-decreasing triples.
- 4 = 4 → but 4 > 3, cannot
- 4 = 3+1 → needs third 0 → (3,1,0)
- 4 = 2+2 → (2,2,0)
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