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Home » The antiderivative of \( 200e^0.05t \) is: - Parker Core Knowledge

The antiderivative of \( 200e^0.05t \) is: - Parker Core Knowledge

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 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)

📌 Since the two non-empty groups have different sizes, no symmetry — all assignments are distinct under permutation of archives → 4

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