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This counts ordered assignments: choose the archivist (8 choices), then banquet leader (7), then certifier (6), then dancer (5).
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?
We want the probability that exactly 3 out of 7 segments are occupied, and all 7 birds are assigned to exactly those
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