5. The following is known as the classic "Birthday Problem." Suppose there is a room with a certain number of individuals in it. Ignoring the possibility of leap years and assuming all birthdays are equally likely, find the following:

a) If there are two people in the room, the probability that they do not share the same birthday.

b) If there are four people in the room, the probability that none of them share the same birthday.

c) What is the smallest number of people that could be in the room for the probability that at least two people share a birthday to be above 50%? (Be prepared to have your calculator out.)