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\[ 2x = 60 \] - Midis

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 \boxed{107}

📌 Frage: Ein Ausschuss von 4 Personen soll aus einer Gruppe von 6 Männern und 5 Frauen gebildet werden. Wie viele Möglichkeiten gibt es, den Ausschuss zu wählen, wenn er mindestens eine Frau enthalten muss?

📌 Lösung: Zuerst berechnen wir die Gesamtzahl der Möglichkeiten, 4 Personen aus $6 + 5 = 11$ Personen zu wählen:

📌 \binom{11}{4} = \frac{11 \cdot 10 \cdot 9 \cdot 8}{4 \cdot 3 \cdot 2 \cdot 1} = 330

📌 Nun subtrahieren wir die Anzahl der Ausschüsse **ohne Frauen**, d.h. nur Männer:

📌 \binom{6}{4} = \frac{6 \cdot 5}{2} = 15

📌 Also ist die Anzahl mit mindestens einer Frau:

📌 - 15 = 315

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