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If 41 people are at a party, what is the probability that more than two of...

If 41 people are at a party, what is the probability that more than two of them have the same birthday? Assume that there are 365 days in a year and all days are equally likely to be the birthday of a specific person. Use Taylor series expansion of the exponential function to provide a first-order approximation of the result if necessary.
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