In probability theory, the birthday problem or birthday paradox concerns the probability that, in a set of $n$ randomly chosen people, some pair of them will have the same birthday.
The birthday problem or birthday paradox is a famous problem in combinatorics and probability theory. The problem is often stated as follows:
Suppose there is a classroom full of people. What is the probability that there are two people with the same birthday? How many people does there need to be in the classroom, so that the probability that two people share the same birthday is 50%?
For a popular introduction see the article Probability and the Birthday Paradox in Scientific American.