The set $S = \{1, 2, 3, \dots, 12\}$ is to be partitioned into three sets $A, B, C$ of equal size such that $A \cup B \cup C = S$ and $A \cap B = B \cap C = C \cap A = \emptyset$. The number of ways to partition $S$ is:
- A$\frac{12!}{(4!)^3}$
- B$\frac{12!}{(4!)^4}$
- C$\frac{12!}{3!(4!)^3}$
- D$\frac{12!}{3!(4!)^4}$
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DifficultIIT 1992
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