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Home » From (2): $w_1 = 3w_3 - 4$. - Silent Sales Machine

From (2): $w_1 = 3w_3 - 4$. - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 \binom{5}{2} = \frac{5 \cdot 4}{2} = 10,\quad \binom{7}{2} = \frac{7 \cdot 6}{2} = 21,\quad \binom{12}{4} = \frac{12 \cdot 11 \cdot 10 \cdot 9}{4 \cdot 3 \cdot 2 \cdot 1} = 495

📌 P(X = 2) = \frac{10 \cdot 21}{495} = \frac{210}{495}

📌 Simplificamos la fracción:

📌 \boxed{\dfrac{14}{33}}

📌 Pregunta: ¿De cuántas formas se pueden sentar 8 personas alrededor de una mesa circular si dos de ellas, Ana y Luis, se niegan a sentarse una al lado de la otra?

📌 Solución: En permutaciones circulares, el número de formas de ordenar $ n $ personas alrededor de una mesa es $ (n-1)! $, ya que se fija la posición de una persona para eliminar la simetría rotacional.

📌 Primero, calculamos el total de arreglos sin restricciones:

📌 Ahora, restamos los casos donde Ana y Luis están sentados juntos. Tratamos a Ana y Luis como un solo "bloque". Esto da $ 7 $ unidades para disponer circularmente: el bloque (A-L) y las otras 6 personas. El número de arreglos circulares es:

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