How many committees of five with a given chairperson can be selected from 12 persons?

If 8 boats enter a​ race, how many possibilities are there for the first through third place​ finishers?   ​(enter a whole​ number)

There are 13 qualified applicants for 6 trainee positions in a fast-food management program. How many different groups of trainees can be selected?

A research team of 7 members must be formed from a group of 10 teachers consisting of 3 senior faculty, 4 junior faculty and 3 rookie faculty members. a. In how many ways can the selection be done if the team must include at least 1 senior faculty member? b. In how many ways can the selection be done if the team must include 2 seniors and at least 1 rookie faculty member?

there are 4 districts and 9 individuals available to carry out the survey. Assuming that no one surveys more than one district and each district is surveyed once, how many different assignments of survey takers to districts are possible?

Suppose you are interviewing 25 people in order to fill 5 job vacancies. How many possible choices of 5 people are there to fill those vacancies?

9 athletes are to take part in a race. In how many ways can the first 5 places be filled?

Among 10 student clubs recruiting new members this year, how many ways are there to choose 8 clubs out of 10 to join?

How many ways can a committee of 4 be selected from a club with 10 members?