Question
How many permutations of $\{1,2,3,4,5,6\}$ have(a) exactly 15 inversions?(b) exactly 14 inversions?(c) exactly 13 inversions?
Step 1
This means that the permutation must be the reverse of the original order, which is (6,5,4,3,2,1). There is only 1 permutation with exactly 15 inversions. (b) To have exactly 14 inversions, we need to remove one inversion from the permutation in part (a). We can Show more…
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