We define a bow-tie quadrilateral as a quadrilateral where two sides cross each other. An example of a bow-tie quadrilateral is shown below

Seven distinct points are chosen on a circle. We draw all \(\dbinom{7}{2} = 21\) chords that connect two of these points. Four of these chords are selected at random. What is the probability that these four chosen chords form a bow-tie quadrilateral?

Ben7442era Jul 18, 2020