We compute the single-particle density function and the equilibrium constant using the subspace sampling method (SSM) for three one-dimensional potentials. SSM is a versatile Monte Carlo methodology that partitions configuration space into subspaces. Such partitioning facilitates the sampling of regions of configuration space separated by potential barriers or described by different hamiltonians. We show that SSM can be readily used to compute simultaneously the density function and the equilibrium constant for the subspaces. Furthermore, alternative sampling schemes can be included in the SSM methodology to expedite convergence and minimize the need to search for an optimum parameter set.