Renae, Nexael, Braden, Lovely, and Vanessa are attending a play and want to sit together in a row. In how many ways can these five friends be seated?

Suppose you have a choice of ten TV sets that can be matched with any of six DVR players and eight DVD players. How many different TV/DVR/DVD systems can you assemble?

Most courses offered at a local university worth either 4 or 5 credit hours. The members of the women's basketball team are taking a total of 49 courses that are worth a total of 207 credit hours. How many 4-credit courses and how many 5-credit courses are being taken? The team members are taking... 4-credit hour courses 5-credit hour courses.

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 co-rec team to play in an intramural tournament of indoor soccer should consist of three men and three women. There are five men and ten women to join that team. Within the fifteen people there is a husband and wife. In how many ways can that team be selected if it must contain either the wife or the husband but not both?

A southeast regional salesman has eight destinations that he must travel to this month: Atlanta, Raleigh, Charleston, Nashville, Jacksonville, Richmond, Mobile, and Jackson. How many different possible routes could he take?

If a team of four players must be made from eight boys and six girls, how many teams can be made if they must all be boys?

In the Mindworkzz club all the members participate either in the Tambola or the Fete. 320 participate in the Fete, 350 participate in the Tambola and 220 participate in both. How many members does the club have?

There are 6 boys and 18 girls in a class. A group of 5 students is needed to work on a project. If at least 2 boys are  needed, how many different groups of 5 students are possible?