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\binom123 = 220 - Professionaloutdoormedia

📅 May 13, 2026 👤 scraface

May 13, 2026

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📌 P(n, r) = \frac{n!}{(n-r)!}

📌 Substituting \(n = 5\) and \(r = 3\):

📌 P(5, 3) = \frac{5!}{(5-3)!} = \frac{5 \times 4 \times 3 \times 2 \times 1}{2 \times 1} = 5 \times 4 \times 3 = 60

📌 Therefore, there are \(\boxed{60}\) ways to choose and arrange 3 minerals from 5.

📌 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

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