Example 2 There are $m(m \geqslant 3)$ points on the circumference of a circle, and each pair of points is connected by a chord. If no three chords intersect at the same point (except at the endpoints), how many intersection points are there in total inside the circle?
Solving: Every 4 points on a circle form a convex quadrilateral, whose diagonals (chords) intersect at one point. Therefore, each set of 4 points corresponds to one intersection point. Since no three chords intersect at the same point, different sets of four points correspond to different intersection points. Conversely, let point $P$ be the intersection of chords $A C$ and $B D$, then $P$ is the point corresponding to the set $\{A, B, C, D\}$. Thus, the number of intersection points is the number of 4-element subsets of these $m$ points, which is $C_{m}^{4}$.