About the birthday problem, I already pulished something that I had exeperimented in the classroom, but it is in French: http://irem.univ-reunion.fr/spip.php?article618 (clic on "probl��me des anniversaires" tab). The idea is that if you add say 30 times a "365 atRandom" to a bag (instead of a set) it happens now and then that a number appear more than once. In this classroom, two students actually had the same birthday, and they were eager to know of it happens often, so that they were very active for this exercise.