Start small. Calculate the probability that just one pair of people have different birthdays.
Person A's birthday will only be one day of the year. That leaves only 364 possible birthdays for Person B. That means the probabilty of different birthdays for Person A and Person B, or any pair of people is:
Person A's birthday will only be one day of the year. That leaves only 364 possible birthdays for Person B. That means the probabilty of different birthdays for Person A and Person B, or any pair of people is:
Bring in Person C. Two birthdays are already accounted for by Person A and Person B.
If you multiply each term together, you will get the probability that no one shares a birthday.
And so on....
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