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

Number of ways is 12 C 4 × 8 C 4 × 4 C 4 = ( 4 ! ) 3 12 ! .

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MathematicsPermutation & CombinationnPr & nCrHard2 minPYQ_2007

MathematicsHardsingle choice

The set $S = {1, 2, 3, \dots, 12)$ is to be partitioned into three sets $A, B, C$ of equal size. Thus, $A \cup B \cup C = S, A \cap B = B \cap C = A \cap C = ϕ$ . The number of ways to partition $S$ is

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Answer:

Solution:

Number of ways is $^{12} C_{4} \times^{8} C_{4} \times^{4} C_{4}$ $= \frac{12 !}{( 4 ! ) ^{3}}$ .

Stream:JEESubject:MathematicsTopic:Permutation & CombinationSubtopic:nPr & nCr

⏱ 2mℹ️ Source: PYQ_2007

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