Question

The set $S=\{1,2,\mathrm{3...12}\}$ is to be partitioned into three sets $A$, $B$, $C$ of equal size such that $A\cup B\cup C=S,A\cap B=B\cap C=A\cap C=\varphi$. 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 1

Answer: (A)

$\frac{12!}{{(4!)}^3}$

Number of ways ${=}^{12}{C}_4{\times }^8{C}_4{\times }^4{C}_4=\frac{12!}{(4!{)}^3}$