Question

The set S : = { 1, 2, 3 .........12} is to be partitioned into three sets A, B, C of equal size. Thus

A È B È C = S, A Ç B = B Ç C = A Ç C = f. 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)

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

Answer 2

S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

$\frac{\begin{matrix} 12 \end{matrix}}{\begin{matrix} 4 \end{matrix}\begin{matrix} 4 \end{matrix}\begin{matrix} 4 \end{matrix}}$× $\frac{\begin{matrix} 3 \end{matrix}}{\begin{matrix} 3 \end{matrix}}$ = $\frac{\begin{matrix} 12 \end{matrix}}{(\begin{matrix} 4 \end{matrix})^{3}}$