How many different committees with 4 members can be formed from a group of 9 students? (Order is not important.)

A large research project is looking for more researchers. There are 8 spots open on the research team. There are 10 mathematicians and 14 computer scientists that apply for the team. a. How many different ways can a team of 8 be made for the project? b. How many different ways can a team of 8 be made for the project if the team must contain at least one computer scientist and at least one mathematician.

On a business retreat, your company of 28 executives go golfing. a. You need to divide up into foursomes (groups of 4 people): a first foursome, a second foursome, and so on. How many ways can you do this? b. After all your hard work, you realize that in fact, you want each foursome to include one of the 7 Board members. How many ways can you do this?

The president of the college asked a fraternity to submit a list of 7 students to serve as guides at a school function. They have 19 students who are Available to help. In how many ways can the students be chosen?