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Understanding the Context

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HOT PEPPER Beauty .

bryant gumbel

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Lets compute the total probability by summing over the valid cases.
For a fixed region (say region A), the number of foxes choosing it follows a binomial distribution:
But since only one region can have 6 or more (as $ 6+6 > 8 $), and if 6 choose region A, the other 2 must split between the other two, none exceeding 2, so no overlap.

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