A study of a planar electric double layer (EDL) in the presence of mixtures of electrolyte is presented. In particular, results from the Hyper-Netted-Chain/Mean-Spherical-Approximation (HNC/MSA) theory are compared with Monte Carlo (MC) simulations. In this way, the charge inversion induced by mixtures of multivalent and monovalent counterions is probed. Since overcharging phenomena in nature emerge under such conditions, the role of ion-ion correlations in the EDL appears as a crucial point in this kind of study. Unlike previous related works, a realistic hydrated ion size is used in the HNC/MSA calculations and simulations. In this way, a qualitative agreement between the results obtained from the theory and MC simulations is found. However, some discrepancies arise when the charge inversion is expected to be more noticeable, namely at high surface charges and/or elevated concentrations of multivalent electrolytes. Such differences are explained in terms of an overestimation of the charge inversion by the integral equation (IE) formalism.