Math Lab: Combinations and PermutationsName ______

1. If the NCAA has applications from 6 universitites for hosting its intercollegiate tennis championships in 2008 and 2009, how many ways may they select the hosts for these championships

a) if they are not both to be held at the same university?

b) if they may both be held at the same university?

2. There are five finalists in the Mr. Rock Hill pageant. In how many ways may the judges choose a winner and a first runner-up?

3. In a primary election, there are four candidates for mayor, five candidates for city treasurer, and two candidates for county attorney. In how many ways may voters mark their ballots if they vote in all three races?

4. How many three letter permutations can you make with the word “great”?

5. An art collector, who owns 10 original paintings, is preparing a will. In how many ways may the collector leave these paintings to three heirs?

A class of 20 students is traveling to the Museum of Science for the day.

Find the number of permutations or combinations for each example:

6. Find the number of ways they can sit on the bus. Assuming there is a separate seat for each student.

7. They can view the latest exhibit in groups of 5. How many different groups can be assembled?

8. They will visit the cafeteria in groups of 8. How many different groups can be assembled?

9. The IMAX Theater has 10 seats available. How many different groups can attend?

10. To open your locker, you must dial a sequence of three numbers called the lock’s combination. Given that there are 40 numbers on a lock, how many different locker combinations are there?

11. Ten band directors at a summer band camp are planning to give a performance. One of the pieces they want to play calls for a Flute, an oboe, a bassoon, and a clarinet. Each of the band directors can play all four instruments. How many different quartets can they have?

12. Eight friends go to the movies and Mike insists on being third in line to get tickets. If his wife always stands in front of him in line, how many ways can the 8 friends line up at the ticket window?

13. A baseball team has 25 players on its roster. How many ways are there to pick nine starters?