Five friend compare their dates of birth. In answering the following questions, assume that birthdays are distributed evenly across months.
1. In how many ways can months of birth be assigned to the five friends?
2. In how many ways can months of birth be assigned to the five friends so that they all have different birth months?
3. Suppose that birthdays are evenly distributed across the months. What is the probability that all five friends have different birth months?
4. What is the probability that at least two of the friends have the same birth month?
5. What is the probability that three of the friends are born in January and two are born in February?