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Question: Answered & Verified by Expert
The set $S=\{1,2,3, \ldots, 12)$ 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
MathematicsPermutation CombinationJEE MainJEE Main 2007
Options:
  • A
    $\frac{12 !}{3 !(4 !)^3}$
  • B
    $\frac{12 !}{3 !(3 !)^4}$
  • C
    $\frac{12 !}{(4 !)^3}$
  • D
    $\frac{12 !}{(3 !)^4}$
Solution:
2165 Upvotes Verified Answer
The correct answer is:
$\frac{12 !}{(4 !)^3}$
Number of ways is ${ }^{12} \mathrm{C}_4 \times{ }^8 \mathrm{C}_4 \times{ }^4 \mathrm{C}_4$
$=\frac{12 !}{(4 !)^3}$.

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