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Home » \cdot 600 = 390625 \cdot 6 \cdot 100 = (2,343,750) \cdot 100 = 234,375,000, - Sterling Industries

\cdot 600 = 390625 \cdot 6 \cdot 100 = (2,343,750) \cdot 100 = 234,375,000, - Sterling Industries

📅 April 18, 2026 👤 scraface

Apr 18, 2026

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📌 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?

📌 Since the order of visiting the zones matters (it’s a path), we compute the number of permutations of 7 zones taken 4 at a time:

📌 P(7, 4) = \frac{7!}{(7-4)!} = \frac{7!}{3!} = 7 \times 6 \times 5 \times 4 = 840

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