Consider a polygon of n sides determined by the n noncollinear vertices A, B, C, D, and so...

Consider a polygon of n sides determined by the n noncollinear vertices A, B, C, D, and so on.

a) Choose any vertex of the polygon. To how many of the remaining vertices of the polygon can the selected vertex be joined to form a diagonal?

b) Considering that each of the n vertices in (a) can be joined to any one of the remaining (n − 3) vertices to form diagonals, the product n(n – 3) appears to represent the total number of diagonals possible. However, this number includes duplications, such as and . What expression actually represents D, the total number of diagonals in a polygon of n sides?