We consider the single and multiple photoionization processes in a fullerene molecule. The quantum states of C₆₀ are calculated within the Hartree-Fock and the frozen-core approximations. For the description of multiple photionization probabilities, statistical energy deposition (SED) model was improved and used in addition. The advantage of the SED model is that it is simple enough to be applied to polyatomic systems, where more elaborate calculations are hardly feasible. We account for the electron-electron interaction responsible for the multiple ionization within the random phase approximation with exchange that describes the dynamical polarization of the electronic cloud of the target. As a result, different multi-electron ionization cross-sections of C₆₀ in the photon energy range  10-250 eV are compared, analyzed, and their orders of magnitude are estimated. We also discuss the diffraction of the photoelectron wave on the fullerene shell which results in osciallations in the photionization cross-section as a function of the photon energy.