Q. The set $S = \{ 1,\ 2,\ 3,\ \ldots,\ 12\}$ is to be partitioned into three sets $A,\ B,\ C$ of equal size Thus, $A \cup B \cup C = S$ $A \cup B = B \cup C = A \cup C = \varnothing$ The number of ways to partition $S$ is
A) $12!/3!(4!)^{3}$
B) $12!/3!(3!)^{4}$
C) $12!/(4!)^{3}$
D) $12!(3!)^{4}$
Explanation
(c)
Required number of ways
$= \ ^{12}C_{4} \times \ ^{8}C_{4} \times \ ^{4}C_{4}$
$= \frac{12!}{8! \times 4!} \times \frac{8!}{4! \times 4!} \times 1 = \frac{12!}{(4!)^{3}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.