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Home » Next-Level Fun: Cheap Date Ideas You’ll Love (No Cash Needed!) - Upplift

Next-Level Fun: Cheap Date Ideas You’ll Love (No Cash Needed!) - Upplift

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 A science fair judge is evaluating projects that require arranging 5 distinct minerals into a display. How many ways can the judge choose 3 minerals to highlight sequentially?

📌 The number of ways to arrange 3 minerals out of 5 in a sequence is a permutation problem, where order matters. The formula for permutations of \(r\) items from \(n\) is:

📌 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 \(\binom{8}{4}\).

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