There is a lot of information on the web about how to calculate the probability that, in an arbitrarily-sized group, 2 people will share a birthday. However, I am trying to determine the probability that a larger number of people are born on a specific day (e.g., a group of people have a birthday today, as opposed to "sharing" a birthday any time during the year). I can't find anything on this point. I am trying to address this problem in the context of the following example: Assuming a group of 800 people, what are the odds that 10 people in that group have a birthday today? The probability that any particular one of those 800 people has a birthday today is 1/365. The probability that any particular one does not have a birthday today is 364/365. We want exactly ten people to have a birthday today, and the probability of any 10 having a birthday today and any 790 not having a birthday today is ((1/365)^10)*((364/365)^790). However, this needs to be multiplied by 800!/10!790!, because that is the number of combinations meeting the specified criteria. Does this reasoning make sense? Many thanks.