The set S={1,2,3,…12} is to be partitioned into three sets A, B, C of equal size. Thus A∪B∪C=S, A∩B=B∩C=C∩A=ϕ The number of ways to partition S is

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

1. A

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

2. B

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

3. C

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

4. D

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

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Solution:

Each of the three sets  contains exactly elements.
Thus, the number of ways of partitioning the set $S$ is

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