The equilibrium probability distribution of N methane molecules adsorbed in the interior of n alpha cages of the ZK4 zeolite, the all-silica analogue of zeolite A, is modeled by a modified hypergeometric distribution where the effects of mutual exclusion between particles are extracted from long molecular dynamics simulations. The trajectories are then analyzed in terms of time-correlation functions for the fluctuations in the occupation number of the alpha cages. The analysis digs out the correlations induced by the spatial distribution of the adsorbed molecules coupled with a migration mechanism where a molecule can pass from one a cage to another, one-by-one. These correlations lead to cooperative motion, which manifests itself as a nonexponential decay of the correlators. Our results suggest ways of developing improved lattice approaches that may be useful for studying diffusion in much larger systems and for a much longer observation time.