Probability question: names in hats

[robvalue]

I started doing the tree for 5 people. It's not too bad. I noticed a couple of things:

1) Any situation where you're left with 4 and 5 for the last two players is an instant lose. Player 4 must take number 5, and so it's over.

2) There is a lot of repetition in the tree. I think Aractus was referring to this with his notation. You end up with several ways of getting to the same set of numbers left (such as 3 and 5, say). So from that point, it's only necessary to continue one of these branches to completion and then you can collect together the probability of getting to that position.