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Home » \[ \sqrt150 \approx 12.247 \] - Nelissen Grade advocaten

\[ \sqrt150 \approx 12.247 \] - Nelissen Grade advocaten

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 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.

📌 Question: A science fair judge evaluates 7 student projects, each judged on creativity (C), scientific rigor (R), and presentation (P), with each project receiving a score in each category: high (H) or low (L). The judge considers a project Exceptionally Strong if it receives high scores in at least 5 of the 3 categories. Assuming each score is independently high with probability $ \frac{1}{2} $, what is the probability that exactly 3 out of the 7 projects are Exceptionally Strong?

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