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Two brown birds adjacent on a wire

Question

Eight birds, two brown and six red, settle on a power line in a uniformly random order. How likely is it that the brown pair end up perched right next to each other?

Short answer

1/41/4. There are (82)=28\binom82=28 equally likely pairs of positions for the brown birds, and 7 of those pairs are adjacent, giving 728=14\tfrac{7}{28}=\tfrac14.

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