The set \[S=\{1,2,3,...,12\}\] is to be partitioned into three sets, A, B, C of equal size. Thus\[A\cup B\cup C=S,A\cap B=B\cap C=A\cap C=\phi \]. The number of ways to partition S is

The set \[S=\{1,2,3,...,12\}\] is to be partitioned into three sets, A

1.	The set \[S=\{1,2,3,...,12\}\] is to be partitioned into three sets, A, B, C of equal size. Thus\[A\cup B\cup C=S,A\cap B=B\cap C=A\cap C=\phi \]. 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.	\[\frac{12!}{3!{{(4!)}^{4}}}\]
Answer» B. \[\frac{12!}{{{(4!)}^{4}}}\]

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The set \[S=\{1,2,3,...,12\}\] is to be partitioned into three sets, A, B, C of equal size. Thus\[A\cup B\cup C=S,A\cap B=B\cap C=A\cap C=\phi \]. The number of ways to partition S is

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