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Home » "The Crow Comic Shocked Us All—Here’s Why You Can’t Stop Reading It! - Blask

"The Crow Comic Shocked Us All—Here’s Why You Can’t Stop Reading It! - Blask

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 \]Pregunta: ¿Cuántas disposiciones distintas se pueden hacer con las letras de la palabra "MATHEMATICS" si todas las vocales deben estar juntas?

📌 Solución: Para resolver este problema, primero identificamos las vocales en "MATHEMATICS", que son A, A, E, I. Las trataremos como una sola unidad o bloque. Así, las letras se convierten en: (AAEI), M, T, H, M, T, C, S. Esto nos da 8 unidades para organizar, teniendo las letras M y T cada una repetida dos veces.

📌 El número de formas de organizar estas 8 unidades es:

📌 \frac{8!}{2! \cdot 2!} = \frac{40320}{4} = 10080

📌 Ahora, dentro del bloque (AAEI), las vocales A, A, E, I pueden organizarse entre sí. Dado que A se repite dos veces, el número de disposiciones distintas de las vocales es:

📌 Luego, multiplicamos las dos cantidades:

📌 \times 12 = 120960

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