The set S = {1,2,3,.....,12} is to be partitioned into three sets A, B and 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

Solution :

first we choose 4 numbers from 12 numbers, then 4 from remaining 8 numbers, and then 4 from remaining 4 numbers

So, Required number of ways

= \(^{12}C_4\) x \(^8C_4\) x \(^4C_4\)

= \(12!\over (4!)^3\)