From a club of 19 ​people, in how many ways can a group of four members be selected to attend a​ conference?

How many different selections of three books can be made from a set of fifteen books?

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.

A club has 11 members. Five are to be chosen to go as a group to a national meeting. If the club contains 7 men and 4 women, how many distinct groups of five contain at most two women?

From a group of 20 people, 12 are selected to serve on a jury during a trial. How many different ways can a jury of 12 be selected?

A teacher had chooses 3 of 22 students to help clean the room after school. In How many ways can the students be selected?

Suppose that 15 athletes are competing in a final at the Olympics. In how many ways can the medals be awarded for this race; that is, how many different ways may the racers finish first, second, and third?

At family gathering were the following people:one grandfather, one grandmother,two father's,two mother's,four children,three grandchildren,one brother,two sisters,two sons ,two daughters ,one father-in law,one mother in law,one daughter in law.but not as many people attended as it sounds.how many were there,and who were they?

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?

A city soccer league has 8 teams.  In how many ways could the league assign first, second, and third-place trophies at the end of the season?