The aim of this work is to investigate the population inversion of binary asymmetric Leonard-Jones mixtures inside nanoslit pores due to confinement effects for both vapor and liquid phases. For this purpose we have used mean field fundamental measure theory, and the effect of different parameters such as interaction strength and size ratios of the components, confinement size, and thermodynamic state on the population distribution of molecules have been studied. It has been shown that in the case of bulk liquid mixtures, increasing the role of confinement effects can lead to preferential adsorption of the component with larger size and weaker intermolecular interactions into the nanopore in spite of its minority in the bulk which is referred as population inversion. This population inversion phenomenon is terminated by a sudden condensation which, interestingly, involves a simultaneous adsorption and desorption for more and less bulk concentrated species, respectively. We have demonstrated that this condensation phenomenon shifts to higher bulk densities with increasing the role of confinement effects such that in some cases population inversion is observable for the whole range of densities. In consideration of the conditions in which vapor Leonard-Jones mixtures undergo capillary condensation, the population distribution of components in the vapor- and liquidlike phases was studied. It has been shown that variation of parameters such as interaction strength and size ratios, temperature, and confinement size can lead to conditions in which capillary condensation is accompanying with a population inversion phenomenon. In these cases, whereas the composition of vaporlike phases is the same as bulk fluid, liquidlike phases are richer in the component with less bulk concentration.