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side of a convex quadrilateral, from vertices of regualr 195-gon

Source: Polish MO Recond Round 1985 p3

September 9, 2024
combinatoricscombinatorial geometrygeometry

Problem Statement

Let L L be the set of all polylines ABCDA ABCDA , where A,B,C,D A, B, C, D are different vertices of a fixed regular 19851985 -gon. We randomly select a polyline from the set LL. Calculate the probability that it is the side of a convex quadrilateral.
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