Consider the electronic states of a carbon atom ($Z=6$). Which statements are correct?

1. APlacing both $2p$ electrons in one $2p$ orbital with opposite spins does not violate the Pauli principle but violates Hund's rule for the ground state.
2. BPlacing both $2p$ electrons in one $2p$ orbital with the same spin violates the Pauli principle.
3. C$1s^{2}2s^{1}2p^3$ is the ground state because it has more unpaired electrons and hence more exchange energy.
4. D$1s^{2}2s^{2}2p^2$ with the two $2p$ electrons in different orbitals with parallel spins is the ground state.