Using 23 children in the same class you calculate the probability of none have the same birthday and then subtract that from 1.

See here for example :

http://en.wikipedia.org/wiki/Birthday_problem
This looks a lot simpler to understand :

http://www.agenarisk.com/resources/probability_puzzles/birthdays.shtml
From memory I first discovered this in one of Martin Gardner's articles back in the late sixties / early seventies. Either that or a book on reasonably basic probability.

Good idea of yours to post - gets the old grey cells working.