Investigation of competitive adsorption is carried out using the Xe-Ar mixture in zeolite NaA as a model system. The Xe-n clusters are trapped in the alpha cages of this zeolite for times sufficiently long that it is possible to observe individual peaks in the NMR spectrum for each cluster while the Ar atoms are in fast exchange between the cages and also with the gas outside. The Xe-129 nuclear magnetic resonance spectra of 12 samples of varying Xe and Ar loadings have been observed and analyzed to obtain the Xe-129 chemical shifts and the intensities of the peaks which are dependent on the average argon and xenon occupancies. The detailed distributions, f(XenArm), the fractions of cages containing n Xe atoms and m Ar atoms cannot be observed directly in this system,that is, individual peaks for XenArm mixed clusters are not observed in the NMR spectrum. This information is, however, convoluted into the observed Xe-129 chemical shifts for the Xe-n peaks and the distributions P-n, the fraction of cages containing n Xe atoms, regardless of the number of Ar atoms, obtained from their relative intensities. Grand canonical Monte Carlo (GCMC) simulations of mixtures of Xe and Ar in a rigid zeolite NaA lattice provide the detailed distributions and the average cluster shifts, as well as the distributions P-n. The agreement with experiment is reasonably good for all 12 samples. The calculated absolute chemical shifts for the Xe-n peaks in all samples at 300 K range from 75 to 270 ppm and are in good agreement with experiment. The GCMC results are compared with a strictly statistical model of a binary mixture, derived from the hypergeometric distribution, in which the component atoms are distinguishable but equivalent in competition for eight lattice sites per cage under mutual exclusion. The latter simple model introduced here provides a limiting case for the distributions, with which both the GCMC simulations and the properties of the actual Xe-Ar system are compared.