Question

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

• A. $\frac{12!}{3!\left(4!\right)^{3}}$
• B. $\frac{12!}{3!\left(3!\right)^{4}}$
• C. $\frac{12!}{\left(4!\right)^{3}}$
• D. $\frac{12!}{\left(3!\right)^{4}}$

Answer 1

Answer: (C)

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

Answer 2

Number of ways is $^{12}C_{4}\times^{8}C_{4}\times^{4}C_{4}$ $=\frac{12!}{\left(4!\right)^{3}}$