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\sin heta = n \sin \phi - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Question: A hydrologist is studying a river system with 6 tributaries. She wants to select 3 tributaries to monitor closely. If two of the tributaries are near a protected wetland and must both be monitored if either is selected, how many valid selections of 3 tributaries are possible?

📌 Let the two special tributaries be $ A $ and $ B $. The condition is: **if either A or B is selected, both must be selected**.

📌 We must count all 3-tributary selections satisfying this rule.

📌 Case 1: Neither A nor B is selected

📌 Then we choose all 3 from the remaining 4 tributaries:

📌 Case 2: Both A and B are selected

📌 Then we choose 1 more from the remaining 4:

📌 Total valid selections:

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