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Home » Substitute back to find \( U(12) \): - Midis

Substitute back to find \( U(12) \): - Midis

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 5Question: A primatologist observes 7 different chimpanzees engaging in a communication ritual where each chimpanzee either vocalizes or gestures, but not both, and at least two chimpanzees must gesture. How many distinct communication patterns are possible?

📌 Solution: Each chimpanzee has 2 choices: vocalize or gesture, but since each must choose exactly one and at least two must gesture, we begin by computing the total number of unrestricted assignments and subtract invalid cases.

📌 Total assignments (each chimp independently chooses vocalize or gesture):

📌 Invalid cases:

📌 0 gesturing (all vocalize): $ \binom{7}{0} = 1 $

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