The k-electron correlation function of a free chaotic electron beam is derived with the spin degree of freedom taken into account. It is shown that this can be expressed with the help of correlation functions for a polarized electron beam of all orders up to k, and the degree of spin polarization. The form of the correlation function suggests that if the electron beam is not highly polarized, observing multiparticle correlations should be difficult. The result can also be applied to chaotic photon beams, the degree of spin polarization being replaced by the degree of polarization.