Suppose that a department contains 10 men and 15 women. How many ways are there to form a committee with sixmembers if it must have the same number of men and women?

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.

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?

In how many ways can a committee of 12 men and 12 women be selected from a panel of 36 men and 40 women?

A group of 13 people consisting of 3 freshmen, 2 sophomores, 4 juniors, and 4 seniors are selected from 6 freshmen, 5 sophomores, 5 juniors, and 7 seniors. How many groups can be formed?

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?

In how many ways can a committee of three men and four women be formed from a group of eleven men and ten ​women?

In a club with 10 male and 11 female members, how many 6-member committees can be selected that have not more than 2 men?