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?

Question

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?

ash2326 · Answer

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

ash2326 · Answer

no of required cases =365*1*1*364*363

anonymous · Answer

Why is it (365)^4 and not (365)^5?

ash2326 · Answer

one 365 got cancelled by the numerator's 365

anonymous · Answer

oh i see.... Thank you so much! :)

ash2326 · Answer

welcome xEnOnn