【Hai Chuan: Thinking Keeps You Young】A Coincidental Birthday
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How many friends do you need to invite to ensure that at least two of them have birthdays on the same day (it doesn’t have to be the same year)? Are 366 people needed?
Xixi, hahaha – live every day well.
No, anyone can be born on any day of the 365 days, so each person has 365 possible birth dates. If there are N people, then those N people have 365 to the power of N possible birth dates. Assuming that a fixed number of M days is required for the birth date, there are C365M ways to choose such a date. For a fixed set of M days, N people have N! possible combinations It’s a matter of probability, so the desired probability P = N! * C(365, M) / (365^N) can only be calculated as a probability; it’s not possible to determine the exact number of people. It’s possible that just one person you invite will do, or it might take hundreds of millions of invitations before finding such a person. In mathematics, similar problems can only have their probabilities calculated; an exact numerical value cannot be determined
Yes, 366 is the smallest number that ensures at least two people share a birthday