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Home » From Seed to Super Garden: Hack Mutations for Supercharged Blooms! - IX Labs

From Seed to Super Garden: Hack Mutations for Supercharged Blooms! - IX Labs

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 \times \frac{1}{36} \times \frac{25}{36} = \frac{150}{1296} = \frac{25}{216}

📌 Por lo tanto, la probabilidad es:

📌 \boxed{\dfrac{25}{216}}

📌 \]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:

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