## [ Combinations and arrangements $\quad]$ $[$ Systems of points and segments (etc.) $)]$ $[\quad$ Rule of product $\quad]$ [ Arbitrary polygons ]

How many diagonals does a convex:
a) 10-gon;
b) $k$-gon $(k>3)$ have?

#
b) Each pair of points forms a segment: a side or a diagonal.

By subtracting the number $k$ of sides from the number $C_{k}^{2}$ of pairs, we get the number of diagonals.

## Answer

a) 35 ; b) $\frac{k(k-3)}{2}$ diagonals.