Bogosort optimization, probability related

I'm coding a question on an online judge for practice . The question is regarding optimizing Bogosort and involves not shuffling the entire number range every time. If after the last shuffle several first elements end up in the right places we will fix them and don't shuffle those elements furthermore. We will do the same for the last elements if the开发者_Python百科y are in the right places. For example, if the initial sequence is (3, 5, 1, 6, 4, 2) and after one shuffle Johnny gets (1, 2, 5, 4, 3, 6) he will fix 1, 2 and 6 and proceed with sorting (5, 4, 3) using the same algorithm. For each test case output the expected amount of shuffles needed for the improved algorithm to sort the sequence of first n natural numbers in the form of irreducible fractions.

A sample input/output says that for n=6, the answer is 1826/189.

I don't quite understand how the answer was arrived at.

This looks similar to 2011 Google Code Jam, Preliminary Round, Problem 4, however the answer is n, I don't know how you get 1826/189.