The set $S=\{1,2,3, \ldots, 12)$ is to be partitioned into three sets $A, B, C$ of equal size. Thus, $A \cup…
The set $S=\{1,2,3, \ldots, 12)$ 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
$\frac{12 !}{3 !(4 !)^3}$
$\frac{12 !}{3 !(3 !)^4}$
$\frac{12 !}{(4 !)^3}$
$\frac{12 !}{(3 !)^4}$
Solution
Number of ways is ${ }^{12} \mathrm{C}_4 \times{ }^8 \mathrm{C}_4 \times{ }^4 \mathrm{C}_4$
$=\frac{12 !}{(4 !)^3}$.