This is a second paper in the series which aims at the study of combinatorial aspects of the quantum inverse scattering method. A bijective correspondence is set between the standard tableaux and the rigged confiegurations, the latter being a novel class of combinatorial objects introduced in the course of our studies of Bethe's equations. This bisection yields a simple Bethe's equations. This bisection yields a simple combinatorial representation for Kostki's polynomials and allows to compute some important functionals defined on the set of standard tableaux.