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Home » Sam Houser’s Hidden Traps: What Successful Businessmen Fear to Admit! - Dyverse

Sam Houser’s Hidden Traps: What Successful Businessmen Fear to Admit! - Dyverse

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Substituting \(n = 6\) and \(r = 2\):

📌 \binom{6}{2} = \frac{6!}{2!(6-2)!} = \frac{6 \times 5}{2 \times 1} = 15

📌 Thus, the number of unique communication events in one day is \(\boxed{15}\).

📌 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

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