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Degeneracy is defined as having two or more quantum states in a quantized energy level. For example, the p orbital has three degeneracies because it has three quantum states (or three orbitals of the same energy). The d orbital has five degeneracies because it has five quantum states (or five orbitals of the same energy).
As many answers have stated, degeneracy refers to the number of possible quantum states on an energy level. A question might ask something like, 'How many degenerate orbitals are there in the p orbital of a carbon atom at ground level?' In this case, there are two degenerate orbitals in the p orbital. This is because there exist two orbitals that are occupied, and both of them have the same number of electrons with the same spin (2p1 and 2p2).
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