The set S={1,2,3,…12} is to be partitioned 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 partition S is

Each of the three sets A, B, C contains exactly  4elements.Thus, the number of ways of partitioning the set S is13! 12C4 8C4 4C4=13!12!4!8!×8!4!4!(1)=12!3!(4!)3