191. Intersection of Diagonals. Find the number of intersection points of the diagonals of a convex $n$-gon.
191. Consider a polygon with $n$ sides, where $n \geqslant 4$. Any four vertices of this polygon define some

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quadrilateral, the diagonals of which coincide with two intersecting diagonals of the original $n$-gon. Conversely, any two intersecting diagonals of the original $n$-gon define some quadrilateral. Therefore, the number of intersection points of the diagonals is $C_{n}^{4}$. Of course, some of these intersection points may coincide.

[Norbert Kaufman and R. H. Koch, A. M. M., 54, 344 (June 1947).]