It is well-known that a solvent can modify the relative importance of the different constituents (electrostatic and dispersion) of non-covalent interactions, but much less is known about how these solvent-induced modifications specifically couple with the polarization of the electronic density and electronic correlation. Here we present a quantum mechanical analysis of the effects of the solvent on the non covalent interactions (both stacking and hydrogen bonding) in base pairs using a hierarchy of combinations between a MP2 correlated description for the base pairs and the polarizable continuum model (PCM) for the solvent. A comparison of the results obtained in these different combinations of increasing accuracy allows us to better analyze the important role played by the coupling between correlated electronic densities and solvent polarization in determining the relative importance of stacking and hydrogen bonding effects.