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GATE | GATE-CS-2006 | Question 24
Given a set of elements N = {1, 2, ..., n} and two arbitrary subsets A⊆N and B⊆N, how many of the n! permutations π from N to N satisfy min(π(A)) = min(π(B)), where min(S) is the smallest integer in the set of integers S, and π(S) is the set of integers obtained by applying permutation π to each element of S?
(A)
(n - |A ∪ B|) |A| |B|
(B)
(|A|2+|B|2)n2
(C)
n! |A∩B| / |A∪B|
(D)
|A∩B|2nC|A∪B|
Answer
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