21.1.1 * Let the arbitrary 3 diagonals of a convex $n$-sided polygon not intersect at the same point inside the polygon. Find the number of intersection points of the diagonals inside the polygon.
According to the problem, a point of intersection $P$ is obtained by the intersection of two diagonals $l$ and $m$, and conversely, two intersecting diagonals $l$ and $m$ determine a point of intersection $P$, thus $P$ and $(l, m)$ can establish a one-to-one correspondence.

Furthermore, the two intersecting diagonals $l, m$ are formed by connecting two pairs of vertices $A, B$ and $C, D$ of a convex $n$-sided polygon, and for any 4 vertices of a convex $n$-sided polygon, there is exactly one pair of diagonals intersecting inside the polygon (as shown in the figure), hence $(l, m)$ can also establish a one-to-one correspondence with the 4-vertex group $(A, B, C, D)$, i.e., $P$ $\leftrightarrow(l, m) \leftrightarrow(A, B, C, D)$. Therefore, the total number of intersection points of the diagonals inside the polygon equals the number of 4-vertex groups of the convex $n$-sided polygon $\mathrm{C}_{n}^{4}$.

Comment: The conclusion in this problem is an important conclusion in combinatorial geometry, and it can be used in the future to solve more complex counting problems in combinatorial geometry.