  We consider the problem of calculation of correlation functions in the
six-vertex model with domain wall boundary conditions. To this aim, we
formulate the model as a scalar product of off-shell Bethe states, and, by
applying the quantum inverse scattering method, we derive three different
integral representations for these states. By suitably combining such
representations, and using certain antisymmetrization relation in two sets of
variables, it is possible to derive integral representations for various
correlation functions. In particular, focusing on the emptiness formation
probability, besides reproducing the known result, obtained by other means
elsewhere, we provide a new one. By construction, the two representations
differ in the number of integrations and their equivalence is related to a
hierarchy of highly nontrivial identities.
