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📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 An entomologist is studying a group of 8 different insect species, and wants to form a committee of 4 species to focus on pollination. How many different committees can be formed?

📌 To find the number of different committees that can be formed, we calculate the number of combinations of 4 species from 8. This is given by the binomial coefficient \(\binom{8}{4}\).

📌 Using the formula for combinations:

📌 \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 \(r = 2\):

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