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Home » This Hidden Tool Transforms How You Create Shapes—Shapesmith Unveiled! - Moon Smoking

This Hidden Tool Transforms How You Create Shapes—Shapesmith Unveiled! - Moon Smoking

📅 May 14, 2026 👤 scraface

May 14, 2026

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📌 Los tres números tienen el mismo residuo: \(\dbinom{17}{3} + \dbinom{17}{3} + \dbinom{16}{3}\) (ya que hay 17 números conresiduo 0, 17 conresiduo 1, y 16 conresiduo 2).

📌 Un número de cada residuo: \(17 \times 17 \times 16\).

📌 Número total de maneras de elegir 3 números: \(\dbinom{50}{3}\).

📌 Probabilidad:

📌 \frac{3\dbinom{17}{3} + \dbinom{16}{3} + 17 \times 17 \times 16}{\dbinom{50}{3}} = \frac{3 \times 680 + 560 + 4568}{19600} = \frac{2040 + 560 + 4568}{19600} = \frac{6168}{19600} = \boxed{\dfrac{1542}{4900}}

📌 Pregunta: ¿De cuántas maneras pueden sentarse 5 miembros distinguibles y 3 no miembros distinguibles alrededor de una mesa circular si se consideran equivalentes las rotaciones y las reflexiones?

📌 Solución: Para arreglos en círculo con reflexión, fijo un miembro para eliminar simetrías rotacionales y de reflexión. Los 4 miembros restantes se pueden arreglar de \(4!\) maneras, y los 3 no miembros de \(3!\) maneras. Total de arreglos:

📌 4! \times 3! = 24 \times 6 = \boxed{144}

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