# 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 $$^4C_4$$

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

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