Two blue birds side by side on a wire

Eight birds, two blue and six yellow, settle on a telephone wire in a uniformly random order, one bird per spot. Find the chance that the blue pair sits in adjacent spots.

$1/4$. The two blue birds occupy a uniformly random pair of the $8$ spots. There are $\binom82=28$ pairs, of which $7$ are adjacent, so the probability is $\tfrac{7}{28}=\tfrac14$.