CO2 molecules has 3N-5=4 vibrational modes (where N is the number of atoms) of which one mode is symmetric?

Question

and the other three are asymmetric .For one mole of CO2,(10^24 molecules),calculate the number of ways that the CO2 can be evenly distributed among these four vibrational modes.
Calculate the entropy of this state.
Compare this result witth the entropy of a state in which all 10^24 molecules are in a single vibrational mode.
Hint:using Sterling's approximation is handy

Answer 1

The answers is 12.