Express the number of diagonals of a convex n-gon.
Each vertex is connected by a diagonal to all others, except for 3 (its two neighbors and itself). Therefore, there are $\frac{\mathfrak{n}(\mathfrak{n}-3)}{2}$ diagonals.

In combinatorics, we often need to count configurations where some are considered equivalent. We then count the total number of possible combinations as if they were different, and divide by the number of combinations that are equivalent. For example, to count his sheep, a shepherd counts the total number of legs and then divides by 4, because by considering that two legs are equivalent if they belong to the same animal, each leg is equivalent to 3 others, so they are grouped by 4.