Problem

Source: USAMO 1983 Problem 1

Tags: AMC, USA(J)MO, USAMO, probability, combinatorics unsolved, combinatorics



On a given circle, six points $A$, $B$, $C$, $D$, $E$, and $F$ are chosen at random, independently and uniformly with respect to arc length. Determine the probability that the two triangles $ABC$ and $DEF$ are disjoint, i.e., have no common points.