Example 5 Suppose that any 3 diagonals of a convex $n$-sided polygon do not intersect at a single point inside the polygon, find the total 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 $m$. Conversely, two intersecting diagonals $l$ and $m$ determine a point of intersection $P$, and $P$ can establish a one-to-one correspondence with $(l, m)$.

Since 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, $(l, m)$ can also establish a one-to-one correspondence with the 4-vertex group $(A, B, C, D)$ (Figure 1-2), i.e.,
$$
P \leftrightarrow(l, m) \leftrightarrow(A, B, C, D) .
$$

Therefore, the total number of intersection points of the internal diagonals $=$ the number of 4-vertex groups of the convex $n$-sided polygon $=$ $C_{n}^{4}$.