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Question: An elementary school student has 5 identical red blocks, 4 identical blue blocks, and 3 identical green blocks. How many distinct towers can she build stacking all 12 blocks in a line?
Solution: The student is arranging a total of $5 + 4 + 3 = 12$ blocks, with indistinguishability within each color. The number of distinct towers is the multinomial coefficient:
Question: An ichthyologist tags 7 fish in a reef: 2 clownfish, 3 parrotfish, and 2 angelfish. If she observes one tagged fish each day for a week, how many distinct sequences of observed species can occur, assuming fish of the same species are indistinguishable?

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