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time for the rose bowl game - Moon Smoking

📅 May 16, 2026 👤 scraface

May 16, 2026

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📌 Now, impose the condition that the Mars episode must come **before** Earth’s.

📌 In any permutation of the 5 episodes, Mars comes before Earth in exactly **half** the cases (since the two are interchangeable in position).

📌 Thus, the number of valid sequences is:

📌 Therefore, the number of distinct sequences where Mars comes before Earth is:

📌 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

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