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?

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.

Jack, Anny and Bella were elected as Executive Officers in their organization. They will be appointed to the posts of Chairman, Treasurer, and Secretary. Since Anis has already been the Secretary for four terms, he is ineligible for the Secretary post. How many possible formations of the posts are there?

A school club has 25 members and needs to elect four officers: a president, vice-president, secretary, and treasurer. How many ways can this be done?