Probability question: names in hats

[robvalue]

Whatever: I'd recommend drawing out a probability tree for the three player case.

Just put in branches that are possible, following the rules of the game. You'll come up with two initial branches, one of which splits into another two. I'll draw it if you like

There is no need to consider possibilities that the rules of the game don't allow. Although you could put all 6 on the tree, and then cross 3 out.