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Suppose there are 5 students in a class. What is the probability of having exactly 3 students who have the same birthday? I am thinking I should have \[365 \times 365 \times 364 \times 363 \times 362\] and then divide all of it by 5. But it doesn't feel right. What should I do to find out the probability?

Mathematics
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three students have b'day o same day, rest two will have on different days so no. of cases =365*364*363 total no. of cases =365*365*365*365*365 so probability=364*363/(365)^4
no of required cases =365*1*1*364*363
Why is it (365)^4 and not (365)^5?

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Other answers:

one 365 got cancelled by the numerator's 365
oh i see.... Thank you so much! :)
welcome xEnOnn

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