  Pascal's triangle will give the number of geodesics from the identity to each
point of ${\bf Z}^2$ if you write it in each of the quadrants. Given a group
$G$ and generating set $\cal G$ we take the {\it Pascal's function} $p_{\cal
G}: G \to {\bf Z}_{\ge 0}$ to be the function which assigns to each $g\in G$
the number of geodesics from $1$ to $g$. We give a general method for
calculating this in hyperbolic groups and discuss the generic case in abelian
groups.
