Given 400 people, estimate the probability that 3 or more will have a birthday on July 4. Assume there are 365 days in a year and each is equally likely to be the birthday of a randomly chosen person.

I have already tried to solve this problem and got e^-3 but that is not correct. I am unsure of where I messed up in my calculations so if you could show step by step then that would be helpful.

And also, how does that calculation differ from this question:

Calculate the probability that at most 1 person in 500 will have a birthday on Christmas. Assume there are 365 days in a year.

Thank you in advance!