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pennsylvania college of technology - inBeat

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 This counts all possible combinations of healthy and unhealthy statuses for 5 trees.

📌 \boxed{32}

📌 A biotech incubator hosts 6 startups. Each startup can either present to a panel of investors on Monday or Tuesday. How many different schedules are possible if exactly 4 startups present on Monday and the remaining 2 on Tuesday?

📌 We need to count the number of ways to choose 4 startups out of 6 to present on Monday (the other 2 automatically go to Tuesday). This is a combination:

📌 \binom{6}{4} = \frac{6!}{4!(6-4)!} = \frac{6 \times 5}{2 \times 1} = 15

📌 Thus, there are 15 possible schedules.

📌 \boxed{15}

📌 An urban planner is designing a walking path through a city park with 7 distinct native plant zones. If the path must include exactly 4 zones and no zone is repeated, how many different paths (sequences) of zones are possible?

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