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