It did take me a good night's sleep to understand it. I was stuck with the exact same question but I see now how the remaining balls are shared among all 8 urns (therefore cases with 11, 12, 13, ... 17 balls are also dealt with).
Thanks again, baptiste 2010/1/12 Rolf Turner <r.tur...@auckland.ac.nz>: > > On 13/01/2010, at 9:19 AM, Greg Snow wrote: > >> How trivial is probably subjective, I don't think it is much above >> trivial. I would not have been surprised to see this question on an exam in >> my undergraduate (300 or junior level) probability course (the hard part was >> remembering the details from that class from over 20 years ago). My >> favorite test question of all time came from that course: "You have a deck >> of poker cards with the 3's removed (and jokers), you deal yourself 5 cards >> at random, what is the probability of getting a straight (not including >> straight flushes)?" >> >> This problem is simpler. Just think of the 8 places in the number as >> urns, and the 17 1's as balls to be put into the urns. One ball has to go >> in the first urn, so you have 16 left, there are choose(16+8-1,8-1) ways to >> distribute 16 undistinguishable balls among 8 distinguishable urns. But that >> includes some solutions with more than 9 balls in an urn which violates the >> digits restriction, so subtract off the illegal counts. If we place 10 >> balls in the first urn, then we have 7 remaining balls to distribute between >> the 8 urns or choose( 7+8-1, 7), If we place 1 ball in the first urn and 10 >> balls in one of the 7 other urns (7*), then there are choose( 6+8-1, 7 ) >> ways to distribute the remaining 6 balls in the 8 urns. Not too complicated >> once you remember (or look up) the formula for urns and balls. > > Sorry to be a thicko --- but doesn't the foregoing solution *leave in* the > possibility > of putting all 17 balls in the first urn? Or 3 balls in the first urn, 12 > in the second, > and the remaining 2 in any of the other six urns? Etc. I.e. don't more > terms have to > be subtracted? > > cheers, > > Rolf Turner > > ###################################################################### > Attention:This e-mail message is privileged and confidential. If you are not > theintended recipient please delete the message and notify the sender.Any > views or opinions presented are solely those of the author. > > This e-mail has been scanned and cleared by > MailMarshalwww.marshalsoftware.com > ###################################################################### > ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.