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Home » \( 7p + 5q = 35 \) - AMAZONAWS

\( 7p + 5q = 35 \) - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 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

📌 \(2,2\) → (2,2,0): Two archives have 2 each, one empty

📌 Number of ways: \(\frac{1}{2} \binom{4}{2} = \frac{1}{2} \cdot 6 = 3\) (choose 2 for first group, but swapping gives same → divide by 2)

📌 Alternatively: number of ways to partition 4 labeled items into two unlabeled pairs:

📌 \frac{1}{2} \binom{4}{2} = 3

📌 \(2,1,1\) → (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.

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