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Home » Therefore, the length of the altitude is \(\boxed{12 \text cm}\). - Deep Underground Poetry

Therefore, the length of the altitude is \(\boxed{12 \text cm}\). - Deep Underground Poetry

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 Question: A hydrologist is analyzing monthly rainfall data for 10 different watersheds. She wishes to select 4 watersheds to compare drought patterns, such that at least one of them has recorded extreme rainfall. If 3 of the 10 watersheds have extreme rainfall data, how many such selections are possible?

📌 First, compute the total number of ways to choose any 4 watersheds:

📌 So the number of valid selections is:

📌 Question: A pharmacologist is analyzing the success rates of 9 drug trials, 3 of which involve a new AI-designed molecule. If she randomly selects 4 trials for detailed analysis, what is the probability that at least one of the selected trials involves the new AI molecule?

📌 Question: A hydrologist is studying the flow rates of 8 rivers. She wants to choose 3 rivers to monitor closely, with the condition that no two selected rivers are adjacent in the list of 8. How many such selections are possible?

📌 We are choosing 3 rivers from 8, labeled 1 through 8, such that no two are adjacent. This is a classic non-adjacent selection problem.

📌 To count the number of such selections, we use the transformation: if we choose 3 rivers such that no two are adjacent, we can think of placing 3 selected markers and 5 non-selected markers in a line, with at least one non-selected between any two selected.

📌 This is equivalent to placing 3 indistinguishable items into 8 positions with no two adjacent. The number of such selections is:

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