I got 3 out of 5 on this question. Where did I go wrong?

10. (5pts) In a university with 3650 students, the professor wanted to know the probability that at least two students shared the same birthday. The probability will be:

total students =3650

total days in a year =365

probability that a student has birthday on a day=1/365

now, for at least 2 students having birthday as same day, there is only 364 days remaining in which 364 students can have birthday, so remaining students must have birthday same to someone other, hence this is an absolute even .

1 - 1/365 = 1 - 365/365*364/365...0/365 = 1

Probability = 1