I don't know whether this question has been asked or not, or if it's on the Wikipedia, and apologies if so but I wanted to know:
Given a group of n people, what is the probability of X people having a unique birthday, i.e. Any particular person (in this group of X people) will not have the same birthday as anyone else.
This goes with the assumptions that birthdays are uniformly distributed. I am looking for an analytical solution, a theorem or wiki that would help and even just a gauge on how hard a problem like this is would be a lot of help.
To clarify, I am looking for something along the lines of Pr(X) = f(n), where f is a function of n.
Thanks