As posted in problems this and this, this is an extension to the derangement problem.
There are n men, n hats, one hat belonging to each person. A random permutation of hats is picked by the men. What is the probability that no person gets the correct hat?
Update (March 6, 2011)
Solution: Posted by Vipul Verma (Engineer at Portware, IIT KGP and University of South California Alumnus) in comments!