27.6. Several points are marked on a circle, $A$ is one of them. Which are there more of: convex polygons with vertices at these points that contain point $A$ or those that do not contain it?
27.6. Any polygon that does not contain point $A$ can be associated with a polygon that does contain point $A$ by adding it to its vertices. However, the reverse operation, i.e., removing vertex $A$, can only be performed for $n$-gons with $n \geqslant 4$. Therefore, there are more polygons containing point $A$ than polygons not containing point $A$, and the difference is equal to the number of triangles with vertex $A$, i.e., $(n-1)(n-2) / 2$.