The Bogolyubov-Born-Green-Yvon (BBGY) equations have been applied to study ionic and mean electrostatic potential distributions around an extremely simplified model of the DNA at low ionic concentrations. Dielectric discontinuities have been taken into account. Results are compared with those obtained in classical Poisson-Boltzmann calculations which neglect the effect of ion-image charge interactions and interionic correlations. It is shown that concentration profiles of divalent counterions an sensitive to the structural elements of the solvent. i.e., the location of the dielectric discontinuities, whereas this effect is negligible for monovalent ions. The numerical method used can be applied to calculate ionic distributions around macromolecules of arbitrary shape placed into dilute solution of multivalent electrolyte.