446.Three Chords, No Crossings
★★★combinatoricsCh. 2 — Axiomatic and Conditional Probability444+ Problems in Probability
Six points are chosen uniformly at random on a circle, then split uniformly at random into three pairs, and a chord is drawn through each pair. What is the probability that no two chords intersect?
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Count the ways to pair 6 points on a circle, and count the non-crossing pairings (a Catalan number).
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