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Home » \[ \binom31 = 3 \] - Dachbleche24

\[ \binom31 = 3 \] - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 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:

📌 Dentro del bloque, Ana y Luis pueden intercambiarse de lugar: 2 maneras.

📌 Así, el número de arreglos donde están juntos es:

📌 \cdot 2 = 1440

📌 Por lo tanto, los arreglos donde Ana y Luis **no** se sientan juntos son:

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