The set s : = { 1, 2, 3 .........12} is to be partitioned into -Turito

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Maths-

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Question

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

$\frac{12!}{(4!)^{3}}$
$\frac{12!}{(4!)^{4}}$
$\frac{12!}{3! (4!)^{3}}$
$\frac{12!}{3! (4!)^{4}}$

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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