How many committees of five can be selected from eight men and seven women if the committees contain two men and three women?

From the 12 male and 10 female sales representatives for an insurance​ company, a team of 4 men and 4 women will be selected to attend a national conference on insurance fraud. In how many ways can the team of 8 be​ selected?

The university senate needs to select an eight-person committee from a pool of 20 faculty members consisting of 14 professors and 6 instructors. How many ways can they select a group of 8 faculty members to form the committee if they must choose exactly 5 professors?

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?

A group of 11 people consisting of 2 freshmen, 1 sophomores, 4 juniors, and 4 seniors are selected from 4 freshmen, 5 sophomores, 5 juniors, and 7 seniors. How many groups can be formed?

How many committees of 4 can be made from a group of 20 republicans and 15 democrats if at least 1 republican and at least 1 democrat must be on the committee?

How many different committees can be formed from 6 teachers and 46 students if In how many ways can the committee of 5 members be selected? the committee consists of 3 teachers and 2 students?

A committee of 4 people need to be selected from twenty numbers of an organization. How many different committees are possible?

Two freshmen and three sophomores from a sorority will attend a conference. If the sorority has 12 freshmen and 15 sophomores, in how many different ways can the conference attendees be selected?

There are 11 girls and 11 boys in a class. A committee of seven is selected for a project. How many possible committees are there containing four girls?