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Imagine a group of people. How big do you think the group would have to be before theres more than a 50% chance that two people in the group have the same birthday? Assume for the sake of argument that there are no twins, that every birthday is equally likely, and ignore leap years. Take a moment to think about it. The answer may seem surprisingly low. In a group of 23 people, theres a 50.73% chance that two people will share the same birthday. But with 365 days in a year, hows it possible that you need such a small group to get even odds of a shared birthday? Why is our intuition so wrong? To figure out the answer, lets look at one way a mathematician might calculate the odds of a birthday match. We can use a field of mathematics known as combinatorics, which deals with the likelihoods of different combinations. The first step is to flip the problem. Trying to calculate the odds of a match directly is challenging because there are many ways you could get a birthday match in a g
