What is the ground-state electron configuration for carbon?

1s^2 2s^2 2p^2

In carbons ground state there are 6 electrons which occupy the the first three sublevels 1s 2s and 2p accordingly. The s sublevel can hold two electrons in its single orbital but is now full. This will repeat itself in the 2s sublevels as it too only has one orbital which can at most support two electrons. Next you get the 2p electron which can support up to six electrons in three orbitals but because carbons is six it has six electrons and we have already used four filling the previous two shells thus carbon only fills this shell with its last two electrons.