  The combined effect of frustration and correlation in electrons is a matter
of considerable interest of late. In this context a Falicov-Kimball model on a
triangular lattice with two localized states, relevant for certain correlated
systems, is considered. Making use of the local symmetries of the model, our
numerical study reveals a number of orbital ordered ground states, tuned by the
small changes in parameters while quantum fluctuations between the localized
and extended states produce homogeneous mixed valence. The inversion symmetry
of the Hamiltonian is broken by most of these ordered states leading to
orbitally driven ferroelectricity. We demonstrate that there is no spontaneous
symmetry breaking when the ground state is inhomogeneous. The study could be
relevant for frustrated systems like $GdI_2$, $NaTiO_2$ (in its low temperature
C2/m phase) where two Mott localized states couple to a conduction band.
