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- 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.
- The number of partitions of 4 with at most 3 parts is 3? Let's list:
- 4 = 4 → but 4 > 3, cannot
- 4 = 2+2 → (2,2,0)
- 4 = 2+1+1 → (2,1,1)
- 4 = 1+1+1+1 → but four parts, more than 3 allowed if maximum per level is 3 and we use at most 3 non-zero? No, level can