You are incorrect that everyone after ends up in the wrong seat after the dummy. The bad passenger has a chance they randomly select their correct seat. But that person only bumps the person who seat they occupy, so it could be they select the last passenger's seat, and everyone is in the correct seat except them and the one person they bumped.
I presume the solution will involve factorials, and it's been a long time since I did those. Or it's a dirty trick and the plane us upside down with no seats and full of tigers.
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