>>14282872You can arrive at both!
The recursive formula is not particularly ugly, it's very simple actually and sort of easy to find by thinking, and perhaps looking at the numbers for small n. Finding the number of cases where no one gets their own papers back(these are called derangements), and consequently the probability that this occurs, for small n is quite easy, just by writing out the permutations and checking. But incase you don't want to bother, here they are [spoiler:lit]for n=1,2,3,4, the number of "derangements is repectively 0,1,2,9, and thus the probabilities are 0,1/2,1/3,3/8[/spoiler:lit]
I have never really seen ? popping up until now, I would be really interested to see where you saw that coming from.
Also if you wish to, you can forget about the probability part of the question all together. The focus is really on the number of derangements, how many ways the professor can hand out the papers such that no one gets their own paper back.
