  Break a stick at random at $n-1$ points to obtain $n$ pieces. We give an
explicit formula for the probability that every choice of $k$ segments from
this broken stick can form a $k$-gon, generalizing similar work. The method we
use can be applied to other geometric probability problems involving broken
sticks, which are part of a long-standing class of recreational probability
problems with several applications to real-world models.
