Using the Thomas-Fermi quark model,a collective,spherically symmetric density of states is created to represent a gas of interacting fermions with various degeneracies at zero temperature.Over a family of pentaquarks,uudc(c),color interaction probabilities were obtained after averaging over all the possible configurations.Three different functions are developed for light,charm,and anti-charm quarks and are assumed to be linearly related by some proportionality constants.Interesting patterns of quark distributions are observed while analyzing the quark function consistency conditions for such constants.