Choosing officers: A committee consists of ten women and eight men. Three committee members will be chosen as officers.
1. How many different choices are possible?
2. How many different choices are possible if all the officers are to be women?
3. How many different choices are possible if all the officers are to be men?
4. What is the probability that all the officers are women?
5. What is the probability that at least one officer is a man?