Let be a permutation over {1,2,...,n} chosen uniformly at random. Show that, for sufficiently large values of n, the probability that has a cycle of size greater than n/2 is in the range [0.2, 0.8]. A cycle of size k in 7 is a sequence a₁, a2,..., ak such that π(ai) i= 1,...,k- 1 and a₁ = ak. = ai+1 for

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