The Student Council at a certain school has ten members. Four members will form an executive committee consisting of a president, a vice president, a secretary, and a treasurer.        In how many ways can these four positions be filled?

A town is forming a committee to investigate ways to improve public safety in the town. The committee will consist of four representatives from the seven-member town council, three members of a five-person citizens advisory board, and three of the 11 police officers on the force. How many ways can that committee be formed? That committee can be formed in ways.

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?

A school club has 25 members and needs to elect four officers: a president, vice-president, secretary, and treasurer. How many ways can this be done?

Leadership positions for a college social club are up for election. Three people are needed to fill the positions of president, vice president, and secretary. Only 10 members are willing to serve in these positions. Each candidate is eligible for each position, and a candidate can only hold one leadership position. How many different ways can the three positions be filled using the 10 possible candidates?

The president of the college asked a fraternity to submit a list of 7 students to serve as guides at a school function. They have 19 students who are Available to help. In how many ways can the students be chosen?

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?

A charity organization has 23 members. They need to choose a president, vice-president, and secretary and they need to choose a 3-person executive board. How many different ways can this be done?

A group of 14 people who are members of an investment club wish to choose a president, vice-president, secretary, and treasurer. How many different ways can this be done?

The University of Ballygobackwards has three colleges: the College of Science, which has 15 staff, 5 of whom are female; the College of Engineering, which has 8 staff, 4 of whom are female; and the College of Arts, which has 17 staff, 6 of whom are female.   Each college has a Dean, who is chosen from the staff in that college.   What is the total number of ways these three Deans can be chosen? Answer:   How many ways can three Deans be chosen, so that at least one of them is female? Answer: