Convex Quadrilateral from Random Chords

Probability · Medium · Free problem
Place
0$ points on a circle and draw all $\binom{10}{2} = 45$ chords between them. You then pick $4$ of these chords uniformly at random. What is the probability that the $4$ selected chords form a convex quadrilateral? (A convex quadrilateral is a four-sided polygon in which every interior angle is less than
80^\circ$.)

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