The set `S={1,2,3,...,12}` is to be partitioned into three sets A,B,C of equal size. Thus `AcupBcupC=S, AcapB=B capC=C capA=phi.` Find the number of ways to partition S.

The set S={1,2,3,....,12} is to be partitioned into three sets A, B, C of equal size. Thus AcupBcupC=S,AcapB=BcapC=phi . The number of ways to partition S is

The set S={1,2,3….12} is to be partitioned into three sets A,BC of equal size Thus A cup B cup C =S ,A cap B =B capC=A cap C=varphi the number of ways to partitions S is

The set S:={1,2,3…..12} is to be partitioned into three sets A,B,C of equal size thus AcupBcupC=S,AcapB=BcapC=AcapC=phi the number of ways to partition S is

The set S={1,2,3,…, 12} is to be partioned into three sets A,B, C of equal size. Thus , A uu B uu C =S , A nn B = B nn C = A nn C = phi . The number of ways to partition S is :