Investigation of competitive adsorption is carried out using the Xe-CH4 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 CH4 molecules are in fast exchange between the cages and also with the gas outside. The Xe-129 nuclear magnetic resonance spectra of nine samples of varying Xe and CH4 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 methane and xenon occupancies. The distributions P-n, the fraction of cages containing n Xe atoms, regardless of the number of CH4 molecules are obtained directly from the relative intensities of the Xe-n peaks. From the observed Xe-129 chemical shift of each Xe-n peak can be obtained the average number of CH4 molecules in the same cavity as n Xe atoms. Grand canonical Monte Carlo (GCMC) simulations of mixtures of Xe and CH4 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 nine samples. The calculated absolute chemical shifts for the Xe-n peaks in all samples at 300 K range from 80 to 230 ppm and are in good agreement with experiment. We also consider a very simple strictly statistical model of a binary mixture, derived from the hypergeometric distribution, in which the component molecules are distinguishable but equivalent in competition for eight lattice sites per cage under mutual exclusion. The latter simple model provides a limiting case for the distributions, with which both the GCMC simulations and the properties of the actual Xe-CH4 system are compared. The ideal adsorbed solution theory gives a first approximation to the selectivity of the adsorption of the Xe and CH4 from a mixture of gases, but starts to fail at high total pressures, especially at low CH4 mole fraction in the bulk.