# Combinatorial Geometry... Or is it Geometrical Combinatorics?

**Discrete Mathematics**Level 3

A 10-cm stick has a mark at each centimeter. By breaking the stick at two of these nine marks at random, the stick is split into three pieces, each of integer length. The probability that those three pieces could be the side lengths of a triangle is \(\frac{a}{b}\). Find \(a+b\).