97

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Understanding the Context

15G

7 ... .

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100

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Solution: First, treat each species as a single block. There are $3!$ ways to arrange the 3 blocks (chimpanzees, gorillas, orangutans). Within each block, the animals can be permuted among themselves: $5!$ for chimpanzees, $3!$ for gorillas, and $4!$ for orangutans. The total number of arrangements is:
Question: A science educator has 7 identical physics flashcards, 5 identical chemistry flashcards, and 3 identical biology flashcards. In how many distinct sequences can the educator distribute one flashcard per day for 15 days?
Solution: This is a multinomial problem where we count the number of permutations of a multiset. The total number of sequences is:

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