Question: A GPS-tagged flock of 7 birds migrates along a route divided into 7 segments. Each bird independently selects one segment to rest in, uniformly at random. What is the probability that exactly 3 different segments are used, and each of these 3 segments is used by at least one bird?

Tue, 05 May 2026 09:02:31 +0000

**A GPS-tagged flock of 7 birds migrates along a route divided into 7 segments. Each bird independently selects one segment to rest in, uniformly at random. What is the probability that exactly 3 different segments are used, and each of these 3 segments is used by at least one bird?** In an era when location-tracking technology reveals patterns in nature and inspiration spoken science, a dynamic question has emerged: How likely is it that a migration route split into 7 segments, with 7 birds each choosing a rest point at random, results in exactly 3 distinct segments being occupied—with no segment left unused? This isn’t just a math puzzle—it reflects how randomness shapes real-world systems, from wildlife behavior to network algorithms and predictive analytics. Understanding this probability means exploring how randomness distributes across discrete choices, a concept increasingly relevant in data science, urban planning, and migration research. ---