1.The set S={1,2,3,…,12}S = \{1, 2, 3, \dots, 12\}S={1,2,3,…,12} is to be partitioned into three sets A,B,CA, B, CA,B,C of equal size. Thus A∪B∪C=SA \cup B \cup C = SA∪B∪C=S, A∩B=B∩C=C∩A=∅A \cap B = B \cap C = C \cap A = \emptysetA∩B=B∩C=C∩A=∅, then the number of ways to partition SSS area.3!(3!)412!\dfrac{3!(3!)^4}{12!}12!3!(3!)4b.12!(4!)3\dfrac{12!}{(4!)^3}(4!)312!c.(3!)412!\dfrac{(3!)^4}{12!}12!(3!)4d.12!3!(4!)3\dfrac{12!}{3!(4!)^3}3!(4!)312!Login to continueOnly logged in users canattempt or see the solution.
