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Solution: The total number of ways to choose 3 studies from 8 is:To count the favorable outcomes where the impactful study is included, we fix that study and choose 2 more from the remaining 7:Thus, the probability that the impactful study is selected is:Question: An electrical engineer designing a high-voltage transformer notes that two circuits reset every 18 and 24 seconds. After how many seconds will they both reset simultaneously?Question: A hydrologist models groundwater flow and finds that two aquifers release water every 30 and 45 days. What is the greatest common divisor of these intervals, representing the largest periodic overlap?Question: A primatologist records primate calls in base-6. What is the base-ten equivalent of the base-six number $432_6$?A researcher is tracking a population of a rare bird species across four distinct regions. She captures and tags 5 birds in each region. If she wants to choose 3 tagged birds for a detailed study, in how many ways can she select them such that at least one bird comes from each region?The total number of ways to choose any 3 birds from 20 is given byWe subtract the cases where the birds do not come from all regions. This involves:All 3 birds from the same region (impossible since there are only 5 in each region, and we need 3 from one).