Example 8 Suppose that no three diagonals of a convex $n$-gon intersect at a single point inside the convex $n$-gon. Find the total number of intersection points of all diagonals inside the shape.
According to the problem, each intersection point $P$ is obtained by the intersection of two diagonals $l$ and $m$, and conversely, two intersecting diagonals $l$ and $m$ determine a point, thus establishing a one-to-one correspondence between $P$ and $(l, m)$.

Moreover, two diagonals $(l, m)$ can also establish a one-to-one correspondence with 4 vertices $(A, B, C, D)$ of the convex $n$-sided polygon (as shown in Figure $11-1$), that is,
$$
P \leftrightarrow(l, m) \leftrightarrow(A, B, C, D),
$$

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