This problem has been floating around for a few years. I heard it from Gary Thompson, Grove City College (Pennsylvania). I don't think anyone has the general solution (with n people). You can use a computer to brute force your way to the answer for small values of n. In particular, the answer for n=10 is 160127/2116800, which is about 0.075645786.
If anyone has any information about solutions, I'd very much like to hear about it.
Jerry Grossman Oakland University
---- Original message ---- >Date: 23 Nov 04 20:51:41 -0500 (EST) >From: John <email@example.com> >Subject: a gift exchange >To: firstname.lastname@example.org > >Ten friends organize a gift exchange. The ten names are put in a hat, >and the first person draws one. If they pick their own name, they >return it to the bag and draw again, until they have a name that is >not their own. Then the second person draws, again returning their >own name if they draw it. This continues down the line. What is the >probability that when the 10th person draws, only their own name will >be left in the bag? > >Any help!!! -- Jerrold W. Grossman, Professor Department of Mathematics and Statistics 346 SEB Oakland University Rochester, MI 48309-4485 248-370-3443 (voice) 248-370-4184 (fax) email@example.com <a href="http://personalwebs.oakland.edu/~grossman/">http://personalwebs.oakland.edu/~grossman/</a>