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Home » Unwrap the Magic: Sweatshirt That’s Taking Christmas Social Media by Storm! - AMAZONAWS

Unwrap the Magic: Sweatshirt That’s Taking Christmas Social Media by Storm! - AMAZONAWS

📅 March 6, 2026 👤 scraface

Mar 06, 2026

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📌 A historian is organizing 4 rare manuscripts into 3 indistinguishable role-based archives: Royal, Scholarly, and Commercial. Each manuscript must be assigned to exactly one archive. How many distinct ways can the manuscripts be assigned, considering only the number per archive matters?

📌 We are assigning 4 distinguishable manuscripts to 3 indistinguishable archives, where only the counts per group matter (i.e., the assignment is determined by a partition of 4 into at most 3 parts, and the manuscripts are labeled, so we count labeled partitions into unlabeled boxes).

📌 We list all integer partitions of 4 into at most 3 parts, where order of parts does not matter (since archives are indistinguishable), and then for each, compute the number of ways to assign labeled manuscripts accordingly.

📌 The valid partitions of 4 into at most 3 parts (each part ≥ 1, since all manuscripts are assigned):

📌 \(4\) → (4,0,0): All 4 in one archive

📌 Number of ways: \(\binom{4}{4} = 1\), and only one way to assign indistinct labels under symmetry → 1

📌 \(3,1\) → (3,1,0): One archive has 3, another has 1

📌 Number of ways: \(\binom{4}{3} = 4\) (choose 3 to go to the 3-element archive)

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