From among the 33 students in a class, one leader and one class representative are to be appointed. In how many ways can this be done?Choices:- 1056 1024 958 1256

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?

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?

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.)

Our Indiscrete Mathematics course has21 students from the the College of Arts, 15 of whom are female;26 students from the the College of Engineering and Informatics, 7 of whom are female;31 students from the the College of Science, 12 of whom are female.How many ways can we choose a single class rep?Answer: How many ways can we choose three reps, one from each of the three Colleges?Answer: How many ways can we choose three reps, one from each of the three Colleges, so that exactly one is female?Answer:

The student government is holding elections for president. There are 4 candidates (labeled A, B, C, and D for convenience). The preference for the election is as follows:Candidates Ranking Ranking Ranking Ranking Ranking RankingA 4 3 2 1 1 3B 3 1 3 3 4 2C 1 2 4 2 3 4D 2 4 1 4 2 1# of votes 120 50 40 90 60 100Questions:How many voters voted in this election?How many voters are needed for a majority? For a plurality?