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Q.

'A' is a set containing 'n' different elements. A subset P of 'A' is chosen. The set 'A' is reconstructed by replacing the elements of P. A subset 'Q' of 'A' is again chosen. The number of ways of choosing P and Q so that P∩Q contains exactly two elements is

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a

nC3⋅2n

b

nC2⋅3n−2

c

3n−2

d

none of these

answer is B.

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Detailed Solution

Two elements for set P∩Q can be selected in nC2ways. Each of the remaining (n - 2) elements can be put in any of the three sets P∩Q′,P′∩Q or (P∪Q)′. So, total number of subsets nC2×3n−2

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'A' is a set containing 'n' different elements. A subset P of 'A' is chosen. The set 'A' is reconstructed by replacing the elements of P. A subset 'Q' of 'A' is again chosen. The number of ways of choosing P and Q so that P∩Q contains exactly two elements is