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Home » -3x + 2z = 5 \quad \text(2)\\ - IX Labs

-3x + 2z = 5 \quad \text(2)\\ - IX Labs

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 #### Case 2: 1 red, 2 green, 1 blue

📌 \binom{5}{1} \cdot \binom{7}{2} \cdot \binom{3}{1} = 5 \cdot 21 \cdot 3 = 315

📌 #### Case 3: 1 red, 1 green, 2 blue

📌 \binom{5}{1} \cdot \binom{7}{1} \cdot \binom{3}{2} = 5 \cdot 7 \cdot 3 = 105

📌 ### Step 3: Total favorable outcomes

📌 \text{Favorable} = 210 + 315 + 105 = 630

📌 ### Step 4: Compute the probability

📌 P(\text{at least one of each color}) = \frac{630}{1365}

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