Ignoring leap years, there are 365 days in a year.

a. If people are born with equal probability on each of the 365 days, what is the probability that three randomly chosen people have different birthdates?

b. If people are born with equal probability on each of the 365 days, what is the probability that 10 randomly chosen people all have different birthdates?

c. If, as in fact turns out to be the case, birth rates are higher during some parts of the year than other times, would this increase or decrease the probability that 10 randomly chosen people have different birthdates, compared with your answer in part (b)?