Question: An environmental remediation team deploys 4 sensors to monitor a polluted site. How many ways can they place the sensors such that no two are adjacent, given the site has 12 distinct monitoring points arranged in a straight line?

Mon, 04 May 2026 03:50:14 +0000

**An environmental remediation team deploys 4 sensors to monitor a polluted site. How many ways can they place the sensors such that no two are adjacent, given the site has 12 distinct monitoring points arranged in a straight line?** As cities and communities increasingly focus on environmental safety, the role of real-time pollution monitoring is growing. With rising awareness of industrial impact on public health, teams face critical decisions on sensor placement—ensuring data accuracy while navigating spatial constraints. A key challenge: placing 4 monitoring sensors across 12 linearly spaced points without any two touching, a task central to optimizing both coverage and compliance. Understanding how to position these devices properly supports smarter, safer site management—crucial in today’s data-driven environmental stewardship. **Why This Question Matters Now** In the U.S., environmental monitoring has gained momentum amid heightened public concern over clean air, water quality, and industrial responsibility. As communities demand transparency, efficient sensor deployment helps bridge information gaps—enabling faster responses to pollution risks. The technical question of arranging non-adjacent sensors reflects broader industry efforts to balance practical monitoring with robust data ethics. With 12 distinct locations on a straight line, the challenge is not just mathematical but operational. Solving it correctly influences monitoring reliability, regulatory reporting, and community trust.