We have studied the predictions of the canonical ensemble concerning the occupation probability for a model with an infinite uniform ladder of degenerate levels. Results show that in the high-degeneracy or high-temperature limit, the canonical ensemble occupation probability would be the same as that under the grand canonical ensemble (given by the Fermi-Dirac distribution). The difference between them is of the order of O(1/g) where g is the degeneracy of the levels. In the low-temperature limit, this difference depends on the corresponding Fermi energy. If the number of electrons is such that the Fermi energy is equal to the energy of a highly degenerate level, then this difference is small. The maximum difference occurs when the Fermi energy is in between two levels. These results are applicable to 1D perfect mesoscopic rings.