Moser's circle problem

Problem

Moser's circle problem asks how many regions a circle can be divided into by choosing $n$ points along the circumference of the circle and joining each pair of points by a straight line. The greatest possible number of regions with $n$ points is given by

$$r_G = { n \choose 4 } + { n \choose 2 } + 1 = \frac{1}{24}(n^4 - 6 n^3 + 23 n^2 - 18 n + 24),$$