Permutations without repetition

Formula = n =

r =

Examples:

1. Ten teams are competing in the final round of the Olympic four-person bobsledding competition.

In how many different ways can 3 bobsledding teams finish first, second, and third to win the gold,

silver, and bronze medal?

2. You are burning a demo CD for your band. Your band has 12 songs stored on your computer.

However, you want to put only 4 songs on the demo CD. In how many orders can you burn 4 of the

12 songs onto the CD?

3. You are considering 10 different colleges. Before you decide to apply to the colleges, you want

to visit some or all of them. In how many orders can you visit:

a) 6 of the colleges?

b) all 10 colleges?

4. How many 4 letter words can be created if repetitions are not allowed?

5. A baseball league has 13 teams, and each team plays each other twice; once at home, and

once away. How many games are scheduled?

Combinations

____________________________ is a way in which a set or number of things can be ordered or arranged.

Order __________________ matter!

Formula: n =

r =

1. The volleyball team has 9 players, but only 6 can be on the court at one time. How many different

ways can the team fill the court?

2. A painter was carrying 7 pails of different colored paint and dropped 4 of them, making a big

mess. How many combinations of colors could he have spilled?

3. Natalie asked the pet store owner for any 5 baby mice from a cage containing 9. How many

possible combinations of mice could be picked?

4. 5 names will be picked from a jar to be on a team. There are a total of 11 names in the jar. How

many different combinations of names can be picked?

5. A class has 10 male students and 12 female students. How many ways can the class select a

committee of four people to petition the teacher not to make the final exam cumulative if the

committee has to have 2 males and 2 females?

6. From a group of 15 smokers and 21 nonsmokers, a researcher wants to randomly select 7 smokers

and 6 nonsmokers for a study. In how many ways can the study group be selected?

Difference between permutations and combinations:

Permutation:

Combination:

Is this a combination or permutation?

1. There are 8 people competing in a race. How many different ways can first, second, and third

place medals be awarded?

2. A pizza shop offers twelve different toppings. How many different three-topping pizzas can be

formed with the twelve toppings?

3. Your English teacher has asked you to select 3 novels from a list of 10 to read as an

independent project. In how many ways can you choose which books to read?

4. The school yearbook has an editor-in-chief and an assistant editor-in-chief. The staff has 15

students. How many different ways can students be chosen for these 2 positions?

5.2 Probability

• How ___________________ something is to happen.

• Many events can’t be predicted with total certainty. The best we can do is say how

____________they are to happen, using the idea of ____________________.

You can express probabilities in three different ways:

Probability ranges from .

All probabilities to 1 or 100.