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## Homework Statement

What is the probability that in a class of N people you will be able to find a trio that shares the same birthday? You only need to find one such trio, and the rest can have whatever birthday they want, as long as it's not the same as that of the chosen trio. So it could be that we have a trio and everyone else has the same birthday or that we have multiple trios. The only thing that matter is that there is one such trio.

## The Attempt at a Solution

[itex]{365\choose 1}{N\choose 3}\frac{1}{365^{3}}\frac{364^{N-3}}{365^{N-3}}[/itex]

I don't see where I could've gone wrong, but Mathworld says that the probability of

*at least*3 people sharing a birthday tops 50% at 88. But with my formula I get a lower number than that despite the fact that what I'm asking is a subset of that. So my probability for the same number N should be lower, thereby requiring a bigger class for the probability to exceed 50%.

What am I doing wrong?