Unless I am mistaken, there is an almost 100% chance (or close to) of at least two people having the same birthday.
Obviously, if n>365, at least two people have the same birthday, or a 100%.
However, if n<365, everyone has a 1 in 365 chance of their birthday (i.e. Bob has a 1/365 chance of being born on Jan 1.)
In order to find the probability of everyone to have a different birthday, you must use exponents or 1/365n. Using this, the answer will become smaller and smaller, very close to zero. That is the probability of everyone having a DIFFERENT birthday, meaning very close to 100% chance of at least two people having the same birthday. 100% * almost 100%= something close to 100%.
Bu don't take my word for it. Let some of the more Senior Members take a look at it.