Section 9-4 Permutations Homework due Feb 9
Main idea: find permutations of a set of objects and find probabilities
Vocabulary: permutation
You and your 2 friends are going to the movies. How many different ways are there to sit in a row?
you – Friend #1 – Friend #2
you – Friend #2 – Friend #1
Friend #1 – you – Friend #2
Friend #1 – Friend #2 – you
Friend #2 – you – Friend #1
Friend #2 – Friend #1 – you
There are 6 way for the three of you to sit in a movie theater row.
A permutation is an arrangement, or listing, of objects in which order is important. In the example above, the arrangement of the 3 classes is a permutation because the order of the classes is different. You can use the Fundamental Counting Principle to find the number of possible permutations.
EX.
In the example above for your 3 classes, we wrote them out. The fundamental Counting Principle shows us to do
Choices for first class * choices for second class that remain * choices for the third class that remain
3 * 2 * 1 = 6 number of permutations of 3 classes
We can do this with any arrangement needed.
EX.
In how many ways can the starting 6 players of a volleyball team stand in a row for a picture?
First person choices * 2nd person choices left * 3rd person choices left *4th person choices left * 5th person choices left * 6th person choices left =
6 * 5 * 4 * 3 * 2 * 1 = 720 different ways to set up the picture with 6 players
We can use a permutation to find the probability in an event.
EX.
In the final event for the WPIAL swimming championships, there are 8 swimmers. If each swimmer has an equally likely chance of finishing in the top two, what is the probability that Sam will come in first and Bob will place second?
n Find the number of arrangements
8 choices for first and 7 choices for second
8 * 7 = 56 number of permutations of the 2 places
Since there is only one way of having Sam in first and Bob in second, the probability is 1/56.
YOU TRY:
1. Two different letters are randomly selected from the letters in the word “math”. What is the probability that the first letter selected is m and the second letter is a?
2. Seven friends are standing in line at the Jack Rabbit. How many ways can they board the ride once it is their turn?
3. You have five seasons of your favorite TV show on DVD. If you randomly select two of them from your collection, what is the probability that you will select season one first and then season two second?
4. You need to make a password of 4 letters of which none is repeated. What is the probability that a person could guess the entire password randomly selecting the four letters?
5. There are 1320 ways for three students to win first, second, and third place during a speech competition. How many students are there in the competition? Explain your reasoning.
Section 9-4 Permutations Homework due Feb 9