So I saw this interesting problem: https://en.wikipedia.org/wiki/Birthday_problem
And I am not the best at probability, so my question is why I cant calculate the probability with
P (2 in n same birthday) = 1/365 * 2/365 * ... * n-1/365
and have to use this instead?
P (2 in n same birthday) = 1 − P (2 in n not same birthday)
I understand how it works, my problem is that this would not be my first approach on this problem.