The set S={1,2,3,...,12}  is to be portioned into three sets A,B,C of equal size. Thus, A∪B∪C=S,  A∩B=B∩C  =C∩A=ϕ . The number of ways to partitions S is

In this case, we have to divide 12 distinct objects in to there equal distguishable groups A,B and C each containing 4 items. This can be done in    12C4×8C4×4C4  i.e., 12444  ways.