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

Question

The set

S = {1,2, 3, \dots, 12}

is to be partitioned into three sets

A, B & C

of equal size, so we can have

A \cup B \cup C = S,

A \cap B = B \cap C = A \cap C = A \cap C = ϕ

. The number of ways to partition

S

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

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

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

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

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