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

S= {1, 2, 3, ….. 12} is to be partitioned into 3 sets A, B, C of equal size containing 4 elements.

 $\mathrm{A}\cap \mathrm{B}=\mathrm{B}\cap \mathrm{C}=\mathrm{C}\cap \mathrm{A}=\varnothing , \mathrm{A}\cup \mathrm{B}\cup \mathrm{C}=\mathrm{S}$

No of partitions 

$$\begin{gathered} ={ }^{12}{\mathrm{C}}_1{\times }^8{\mathrm{C}}_4\times { }^4{\mathrm{C}}_4 \\ =\frac{12!}{{(4!)}^3} \end{gathered}$$