In a permutation \(a_{1}, a_2, \ldots, a_{n}\) of \(n\) distinct integers, an inversion is a pair \((a_{i}, a_{j})\) such that \(i < j\) and \(a_{i} > a_{j}\).

If all permutations are equally likely, what is the expected number of inversions in a randomly chosen permutation of \(1,2,3,\ldots,n \)?

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