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

The set S = {1, 2, 3, . . . , 12} is to be partitioned into three sets A, B and C of equal size. Thus,ABC=S,AB=BC=AC=ϕ
The number of ways to partition S is

  1. A

    12!/3!(4!)3

  2. B

    12!/3!(3!)4

  3. C

    12!/(4!)3

  4. D

    12!/(3!)4

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    Solution:

    .Required number of ways

    =12C4×8C4×4C4=12!8!4!×8!4!4!×1=12!(4!)3

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