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Home » Divide the entire equation by 6: - High Altitude Science

Divide the entire equation by 6: - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 \binom{8 - 3 + 1}{3} = \binom{6}{3} = 20

📌 This formula counts the number of ways to place $k$ non-adjacent indistinct items in $n$ positions.

📌 So, there are 20 ways to choose positions for the 3 A’s such that no two are adjacent.

📌 Step 2: Assign labels to the remaining 5 positions.

📌 Each of the 5 non-A positions can be labeled U, C, or G (3 choices each). So, number of labelings is $3^5 = 243$.

📌 Therefore, total number of valid sequences is:

📌 \times 243 = 4860

📌 Thus, the virologist can observe $\boxed{4860}$ valid genome configurations.

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