How many committees could be formed from 10 students if: there must be 4 or 5 people on the committee? there are 6 people on the committee but John and Mandymust be selected?

A group of 10 people is choosing a chairperson and vice-chairperson.  They put all 10 people's names into a hat.  The first name drawn becomes chair.  The second name drawn becomes vice-chair.  How many possible combinations of chair and vice-chair were there?

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.

At the first tri-city meeting, there were 5 people from town A, 4 people from town B, and 2 people from town C. The council will consist of a chairperson, an assistant chairperson, and a secretary. Note, it is possible for the same person to be assistant chairperson and secretary at the same time. How many ways can they elect a council?

Faculty at a certain university need to create a committee to evaluate the general studies curriculum offered on campus. If there are 25 faculty members and they must select a chair, vice chair, secretary and 4 additional faculty members to be on the committee, in how many ways can the committee be formed?

How many different committees can be formed from 9 teachers and 30 students if the committee consists of 3 teachers and 4 students? C In how many ways can the committee of 7 members be selected?

A committee of 5 people is to be formed from the following 10 people: Len, Mia, Max, Ted, Mel, Ann, Jim, Tim, Moe, Kim. How many combinations are there if there must be exactly 3 people on the committee whose names start with 'M'? Select one: O a. 10C5 O b. Oc. O d. 10P5 (4C3) (6C₂) (4P3) (6P2)

A club will be selecting a committee made up of 4 members. There are 12 eligible members to select from for the committee. In how many different ways can the committee be appointed?

Faculty at a certain university need to create a committee to evaluate the general studies curriculum offered on campus. If there are 34 faculty members and they must select a chair, vice chair, secretary and 5 additional faculty members to be on the committee, in how many ways can the committee be formed?

there are 18 people from the mathematics department and 325 people from the computer science department in a collegea. how many ways are there to get two representatives?so that one person is from the mathematics department and the other is from the computer science department?b. how many ways are there to get one elected representative, from a combination of the two majors?