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Home » No integer solution? But problem implies one. - Roya Kabuki

No integer solution? But problem implies one. - Roya Kabuki

📅 May 8, 2026 👤 scraface

May 08, 2026

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📌 5Alice hat 4 Äpfel, 5 Bananen und 3 Orangen. Wenn sie zufällig eine Frucht nach der anderen isst und alle Früchte desselben Typs nicht unterscheidbar sind, auf wie viele verschiedene Arten kann Alice alle ihre Früchte essen?

📌 Lösung: Wir sollen die Anzahl der unterschiedlichen Sequenzen bestimmen, in denen Alice 4 identische Äpfel (A), 5 identische Bananen (B) und 3 identische Orangen (O) essen kann. Die Gesamtanzahl der essgewerdeten Früchte beträgt $4 + 5 + 3 = 12$.

📌 Da die Früchte desselben Typs nicht unterscheidbar sind, ist die Anzahl der verschiedenen Reihenfolgen gegeben durch den multinomialen Koeffizienten:

📌 \frac{12!}{4!\,5!\,3!}

📌 Wir berechnen dies schrittweise:

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