Math 110 Combinations Extra Practice
1.) In a mathematics class of 15 students, 10 students must do problems at the board on a given day. In how many ways can the 10 students be chosen?
2.) A football coach has 40 candidates out for the squad. In how many ways can the starting 11 be selected without regard to the position that a candidate will play? (Indicate your answer – do not evaluate.)
3.) At registration, a student needs two more courses to complete her schedule. If there are seven possible courses left to pick from, in how many ways can she choose the two courses?
4.) A committee of 11 people, six women and five men, is forming a subcommittee that is to be made up of two women and three men. In how many ways can the subcommittee be formed?
5.) A baseball squad consists of eight outfielders and seven infielders. If the baseball coach must choose three outfielders and four infielders, in how many ways can this be done?
6.) An urn contains six blue marbles and four red marbles.
a.) In how many ways can we select a group of three marbles?
b.) In how many ways can we select two blue marbles and one red marble?
c.) In how many ways can we select two red marbles and one blue marble?
1.) From a group of 12 sprinters and 10 distance runners, a medley relay team is to be formed. The relay team must consist of two sprinters and two distance runners. How many possible medley relay teams are there?
2.) Don has to take a history exam that consists of 15 multiple-choice questions and five essay questions. If Don has to answer 10 multiple-choice questions and two essay questions, in how many ways can he choose them?
3.) A student belongs to a book and music club. This month she has to purchase two books and three CDs. If there are 10 books and 10 CDs to choose from, in how many ways can she choose her purchases?
4.) If six points are drawn on a plane, no three of which are on the same straight line, how many straight lines can be formed? (Two points determine a line.)
5.) How many different committees, each composed of two Democrats, two Republicans, two Liberals, and one Conservative, can be formed from 12 Democrats, 11 Republicans, 5 Liberals, and 3 Conservatives?
6.) The Speaker of the House wants to appoint a committee consisting of three representatives from California, three representatives from Ohio, and three representatives from Illinois. How many different committees can be formed if eight representatives from New York, 10 representatives from California, five representatives from Ohio, and six representatives from Illinois are eligible?
7.) From a group of fifteen birthday balloons, Jason must select three to give to his girlfriend. How many different ways can he select his balloons?
8.) From a class of 28 students, five must be selected to perform a skit. In how many ways can the students be selected?