Permutations And Combinations

Question
CBSEENMA11015584

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 = φ. The number of ways to partition S is-

  • 12!/3!(4!)3

  • 12!/3!(3!)4

  • 12!/(4!)3

  • 12!/(3!)4

Solution

C.

12!/(4!)3

Number of ways
straight C presuperscript 12 subscript 4 space straight x space straight C presuperscript 8 subscript 4 space straight x space straight C presuperscript 4 subscript 4 space equals space fraction numerator 12 factorial over denominator left parenthesis 4 factorial right parenthesis cubed end fraction

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