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Home » Let the number of atom types be \( x \) and \( y \). We know: - Treasure Valley Movers

Let the number of atom types be \( x \) and \( y \). We know: - Treasure Valley Movers

📅 April 19, 2026 👤 scraface

Apr 19, 2026

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📌 \binom{3}{2} = 3

📌 For each such choice, the probability is:

📌 \left(\frac{1}{3}\right)^2 \times \left(\frac{2}{3}\right)^1 = \frac{1}{9} \times \frac{2}{3} = \frac{2}{27}

📌 Multiplying by the number of combinations:

📌 \times \frac{2}{27} = \frac{6}{27} = \frac{2}{9}

📌 \boxed{\dfrac{2}{9}}

📌 An ichthyologist studying fish populations categorizes each fish by size (small, medium, large) and species (trout, salmon, bass). If she observes 4 fish, each independently selected with equal likelihood across all categories, what is the probability that she observes at least one fish of each species?

📌 There are \(3\) species, so the total number of possible species assignments for 4 fish is:

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