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
${{12!} \over {{{(4!)}^3}}}\,\,$
${{12!} \over {{{(4!)}^4}}}\,\,$
${{12!} \over {3!\,\,{{(4!)}^3}}}$
${{12!} \over {3!\,\,{{(4!)}^4}}}$
Solution
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