Explain why the quantum number set (2, 2, -1, -½) is not possible for an electron in an atom.

Answer is: it is not possible, because orbital (azimunthal) quantum number cannot be 2.

The principal quantum number (n) is one of four quantum numbers which are assigned to each electron in an atom to describe that electron's state.

For principal quantum number n=2:

1) azimuthal quantum number (l) can be l = 0...n-1:

l = 0, 1.  

The azimuthal quantum number determines its orbital angular momentum and describes the shape of the orbital.  

2) magnetic quantum number (ml) can be ml = -l...+l.

ml = -1, 0, +1.

Magnetic quantum number specify orientation of electrons in magnetic field and number of electron states (orbitals) in subshells.

3) the spin quantum number (ms), is the spin of the electron.

ms = +1/2, -1/2.

i believe you are right for all except the 3rd ( look at sqdancefan his answer is much better)