A high school has 8 students who want to be class officers. If there are 3 different positions open, how many ways are there for the students to fill them?

A company just hired 8 new secretaries to place in various departments, and the marketing department has 4 different secretarial positions that are currently open. In how many ways can those 4 positions be filled?

At a local elementary school, a principal is making random class assignments for her 8 teachers. Each teacher must be assigned to exactly one job. In how many ways can the assignment be made?

In one school, there are five teachers: teacher A, teacher B, teacher C, teacher D and teacher E. However, only three students (Mr X, Mr Y and Mr Z) have entered the school this year. Note that in this school, one teacher is supposed to teach one student per teacher. In this case, how many ways can the five teachers be allocated to these three students?

A committee of five is to be selected from a class of 30 students.(a) In how many ways can this be done?(b) After the committee is selected, one person is elected chairperson and another is elected secretary. In howmany ways can these positions be filled?

At a certain high school, the Prom Committee is going to choose new members. There are 4 students from the Junior class and 8 students from the Senior class who are willing to be new members. In how many ways can 5 new members be chosen if more than 3 must be from the Senior class?(If necessary, consult a list of formulas.)