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Home » Final answer: $ oxed{rac227} $ - SUpost

Final answer: $ oxed{rac227} $ - SUpost

📅 July 5, 2026 👤 scraface

Jul 05, 2026

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📌 Question: An anthropologist studying a remote community observes that families celebrate festivals using three types of symbolic tokens: red, blue, and green. Each family uses exactly 8 tokens in a sequence during a ritual, and the order matters. If tokens of the same color are indistinguishable, how many distinct sequences can be formed using 3 red, 3 blue, and 2 green tokens?

📌 Solution: We are asked to find the number of distinct permutations of a multiset. The total number of tokens is 8, consisting of 3 red, 3 blue, and 2 green tokens. Since tokens of the same color are indistinguishable, the number of distinct sequences is given by the multinomial coefficient:

📌 Thus, there are 560 distinct ritual sequences possible.

📌 Question: An archaeologist uses a geophysical survey grid divided into 12 distinct zones, each of which can show evidence of ancient structures, tools, or residential remains. If exactly 4 zones show structural remains, 5 show tools, 2 show residential features, and 1 shows nothing, and the zones are distinguishable but the artifacts within each category are indistinguishable, how many distinct configurations of the grid are possible?

📌 Solution: We are distributing 12 distinguishable zones into four categories with fixed counts: 4 structural, 5 tool-related, 2 residential, and 1 none. Since the zones are distinguishable but the artifacts within each category are indistinguishable, we compute the number of ways to assign the categories to zones.

📌 This is equivalent to computing the multinomial coefficient:

📌 Thus, there are 83,160 distinct configurations of the survey grid.

📌 Question: A historian documents 9 scientific observations from a 18th-century journal, recording outcomes as either success, failure, or inconclusive. If each observation yields exactly one result and the sequence of results matters, how many distinct sequences contain exactly 4 successes, 3 failures, and 2 inconclusive outcomes?

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