Maths-
General
Easy

Question

The set S : = { 1, 2, 3 .........12} is to be partitioned into three sets A, B, C of equal size. Thus A unionunion C = S, A intersection B = B  C = A intersection C = ϕ. The number of ways to partition S is -

  1. fraction numerator 12 factorial over denominator left parenthesis 4 factorial right parenthesis to the power of 3 end exponent end fraction    
  2. fraction numerator 12 factorial over denominator left parenthesis 4 factorial right parenthesis to the power of 4 end exponent end fraction    
  3. fraction numerator 12 factorial over denominator 3 factorial left parenthesis 4 factorial right parenthesis to the power of 3 end exponent end fraction    
  4. fraction numerator 12 factorial over denominator 3 factorial left parenthesis 4 factorial right parenthesis to the power of 4 end exponent end fraction    

The correct answer is: fraction numerator 12 factorial over denominator left parenthesis 4 factorial right parenthesis to the power of 3 end exponent end fraction


    S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
    fraction numerator table row 12 end table over denominator table row 4 end table table row 4 end table table row 4 end table end fraction×fraction numerator table row 3 end table over denominator table row 3 end table end fraction = fraction numerator table row 12 end table over denominator left parenthesis table row 4 end table right parenthesis to the power of 3 end exponent end fraction

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