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error 0x800701b1 - AssociationVoting

📅 May 16, 2026 👤 scraface

May 16, 2026

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📌 $ a_3 = 2(a_2 + b_2) = 2(6 + 3) = 18 $

📌 $ a_4 = 2(a_3 + b_3) = 2(18 + 6) = 48 $

📌 $ a_5 = 2(a_4 + b_4) = 2(48 + 18) = 132 $

📌 $ a_6 = 2(a_5 + b_5) = 2(132 + 48) = 360 $

📌 Question: An ichthyologist tags 3 species of fish in a reef: 4 parrotfish, 3 angelfish, and 2 clownfish. Over 9 days, she observes one tagged fish per day, recording only the species. Assuming fish of the same species are indistinguishable, how many distinct observation sequences are possible if no two clownfish are observed consecutively?

📌 We are to count the number of sequences of length 9 using:

📌 Step 1: Arrange non-clownfish first.

📌 Number of distinct arrangements of these 7 items:

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