27.8*. In a convex $n$-gon $(n \geqslant 4)$, all diagonals are drawn, and no three of them intersect at the same point. Find the number of intersection points of the diagonals.
27.8. Any intersection point of diagonals determines two diagonals, the intersection of which it is, and the ends of these diagonals determine a convex quadrilateral. Conversely, any four vertices of a polygon determine one point of intersection of diagonals. Therefore, the number of intersection points of diagonals is equal to the number of ways to choose four points from $n$, i.e., it is equal to $\frac{n(n-1)(n-2)(n-3)}{2 \cdot 3 \cdot 4}$.