in a lecture we derived a formula for the probablilty of at least two people having the same birthday which was as follows,
(365^n -(365!/(365 - n)!))/365^n
why does this not give the probability as 1 for n = 365
if there are 365 people in a room, it is possible for each of them to have a different birthday since there are 365 days to have one on.
366 (or more), on the other hand, evaluates to 1.