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Home » The perimeter of a rectangle is given by \(2 \times (\textlength + \textwidth)\). - ClickBalance

The perimeter of a rectangle is given by \(2 \times (\textlength + \textwidth)\). - ClickBalance

📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 $ 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:

📌 Step 2: Determine available slots for clownfish.

📌 When 7 non-clownfish are placed in a row, there are 8 possible slots for clownfish:

📌 We must place 2 Cs into these 8 slots such that no two are in the same slot (to avoid adjacency).

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