Interesting Problem, not much of a problem, though
Basically, there is a mathematical equation that states the probability of occurrence of a shared birthday in any group of random people. In a group of 23 or more, the probability is 50%+. In a group of 57 or more people, the probability is more than 99%. And, finally, at 366 people, there is a 100% probability factor that two people will have the same birthday.
There is a network attack method based off of this “birthday problem,” known, not surprisingly, as the Birthday Attack.