2. For a permutation Te Sn, consider = 172...n in one-line notation and let the inversions of T be Inv(T) = {(i, j): 1 Tj}. For example, (1, 4) is an inversion of 35412, since the first entry in 35412 (3) is larger than the fourth entry (1). In total, Inv(35412) = {(1,4), (1,5), (2, 3), (2, 4), (2, 5), (3, 4), (3,5)}, so 35412 has 7 inversions. (a) How many inversions are in the permutation 2437165? (b) What is the maximum possible number of inversions for a permutation in Sn?

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