Q24

MCQ2 marks, −0.5

Given a set of elements $N = {1, 2, ..., n}$ and two arbitrary subsets $A⊆N$ and $B⊆N$ , how many of the n! permutations $\pi$ from $N$ to $N$ satisfy $\min(\pi(A)) = \min(\pi(B))$ , where $\min(S)$ is the smallest integer in the set of integers $S$ , and $\pi$ (S) is the set of integers obtained by applying permutation $\pi$ to each element of $S$ ?

(A)

$(n - |A ∪ B|) |A| |B|$

(B)

$(|A|^{2} + |B|^{2})n^{2}$

(C)

$n! \frac{|A ∩ B|}{|A ∪ B|}$

(D)

$\dfrac{|A ∩ B|^2}{^n \mathrm{C}_{|A ∪ B|}}$

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