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Question

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)n^2

c.

n! |A∩B| / |A∪B|

d.

|A∩B|^2nC|A∪B|

Answer: (c).n! |A∩B| / |A∪B|

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Q. 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...

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