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Question: An elementary school student has 5 red blocks, 4 blue blocks, and 3 green blocks—blocks of the same color are indistinguishable. If the student stacks one block per day over 12 days to build a tower, in how many different color sequences can the blocks be stacked?
Solution: We are to count the number of distinct sequences of 12 blocks, where there are 5 red (R), 4 blue (B), and 3 green (G), and blocks of the same color are indistinguishable. This is a permutation of a multiset:
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