Question: An entomologist is studying a population of 12 bees, selecting a sample of 5 for genetic analysis. Among the bees, 4 are tagged for tracking, and we want to ensure at least one tagged bee is included in the sample. How many such samples are possible?

Sat, 18 Apr 2026 09:55:27 +0000

**How an Entomologist Ensures Tagged Bees Are Included When Sampling a Bee Population** Curiosity about pollinators and their vital role in ecosystems is growing across the United States, especially as scientists work to protect vulnerable bee populations. A common challenge in ecological studies involves selecting representative, genetically meaningful samples—particularly when tracking individual bees over time. In one such scenario, researchers tracking a colony of 12 bees must choose a sample of 5 for detailed genetic analysis. Among these 12, 4 bees carry unique tracking tags, and ensuring at least one tagged bee is included transforms this selection into a key statistical consideration. So, how many valid samples meet this requirement? This question reflects real-world priorities in biodiversity monitoring and provides a clear example of intentional sampling design. --- **The Science Behind Selective Sampling**