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Key Insights

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\(2,1,1\) → (2,1,1): One archive has 2, two have 1
Number of ways: Choose the pair: \(\binom{4}{2} = 6\), then assign the remaining two to separate archives. Since the two singles are indistinguishable in size, and archives are indistinguishable, no overcounting — 6 ways.
Total: \(1 + 4 + 3 + 6 = 14\)

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