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📅 April 16, 2026 👤 scraface

Apr 16, 2026

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📌 \binom{8}{4} = \frac{8!}{4!(8-4)!} = \frac{8 \times 7 \times 6 \times 5}{4 \times 3 \times 2 \times 1} = \frac{1680}{24} = 70

📌 Thus, the number of different committees that can be formed is \(\boxed{70}\).

📌 A primatologist is observing a group of 10 primates and wants to form pairs for a study. How many distinct pairs of primates can be formed?

📌 To determine the number of distinct pairs, we use combinations to choose 2 primates from 10. This is calculated as \(\binom{10}{2}\).

📌 Substituting \(n = 10\) and \(r = 2\):

📌 \binom{10}{2} = \frac{10!}{2!(10-2)!} = \frac{10 \times 9}{2 \times 1} = 45

📌 Thus, the number of distinct pairs of primates is \(\boxed{45}\).

📌 An entomologist is cataloging insects and wants to select 3 from a group of 12 different species for a detailed genetic analysis. How many ways can the entomologist choose the species?

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