  We state and prove several theorems that demonstrate how the coordinate Bethe
Ansatz for the eigenvectors of suitable transfer matrices of a generalised
inhomogeneous five-vertex model on the square lattice, given certain conditions
hold, is equivalent to the Gessel-Viennot determinant for the number of
configurations of $N$ non-intersecting directed lattice paths, or vicious
walkers, with various boundary conditions. Our theorems are sufficiently
general to allow generalisation to any regular planar lattice.
