Verified Solution • 2025–26 Session moderate

QJEEM07Ma0939: JEE Main 2007 Mathematics - Class 11 JEEM07Ma0939 Solution: The set S = {1, 2, 3, ........., 12} is to be partitioned into…

The set S = {1, 2, 3, ........., 12} is to be partitioned into three sets A, B, C of equal size. Thus A∪B∪C=S, A∩B=B∩C=A∩C=ϕA \cup B \cup C = S,\,A \cap B = B \cap C = A \cap C = \phi . The number of ways to partition S is

Multiple Choice Options

  • A 12!(4!)3  {{12!} \over {{{(4!)}^3}}}\,\,
  • B 12!(4!)4  {{12!} \over {{{(4!)}^4}}}\,\,
  • C 12!3!  (4!)3{{12!} \over {3!\,\,{{(4!)}^3}}}
  • D 12!3!  (4!)4{{12!} \over {3!\,\,{{(4!)}^4}}}

Step-by-Step Verified Solution

The total number of ways is

12C4×12−4C4×12−4−4C4=12C4×8C4×4C4=12!(4!)3{}^{12}{C_4} \times {}^{12 - 4}{C_4} \times {}^{12 - 4 - 4}{C_4} = {}^{12}{C_4} \times {}^8{C_4} \times {}^4{C_4} = {{12!} \over {{{(4!)}^3}}}

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