12­7_Counting_Methods_and_Permuations_2010_2web.notebook
Warmup
December 07, 2010
12­7: Counting methods and Permutations
You roll a standard six­sided die. Find the probability of each event.
Goal: Apply the multiplication counting principle and
permutations to solve counting problems.
Feb 27­3:44 PM
Multiplication Counting Principle
Feb 28­9:55 AM
Tree Diagram
You are trying to get dressed for school but don't know what to wear. You have 3 shirts, 2 pairs of pants, and 2 pairs of shoes to choose from. How many different outfits could you wear?
What is one method could we use to solve this problem?
Feb 27­5:28 PM
How many different outfits could you make if you have 8 shirts, 5 pants, 6 socks and 3 shoes?
Feb 28­10:16 AM
Important Idea!!!!!
Multiplication Counting Principle: The number of possible
outcomes for an event is found by multiplying the number
of choices at each stage of the event.
Feb 28­10:16 AM
Feb 28­10:16 AM
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12­7_Counting_Methods_and_Permuations_2010_2web.notebook
You can make one selection from each category; Burrito Size, Tortilla, Filling, and Salsa at Big City Burrito. How many different burritos could you order?
Feb 28­10:16 AM
December 07, 2010
How many different 4 letter arrangements can you make from the letters in the word HEAR without reusing any letters?
Feb 28­10:16 AM
Another kind of counting problem involves finding the number of possible arrangements of the items in a set. There are 4 possible choices for the first letter: H, E, A, and R
After one of these letters is put in the first space, there are only 3 choices left.
H EA R
After you have filled spaces 1 and 2, there are only 2 letter choices left
After you have filled spaces 1, 2, and 3, there is only 1 letter left
Nov 30­8:33 AM
Permutations
When the order of the items in a set matters, this arrangement is called a permutation.
Feb 28­11:03 AM
Permutation Examples
How many different batting orders can you have with 9 baseball players?
Feb 28­11:39 AM
Feb 28­11:45 AM
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12­7_Counting_Methods_and_Permuations_2010_2web.notebook
Permutations can involve a special mathematical symbol, !. This symbol is called a FACTORIAL. This is what it means:
6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
Try this example:
A swimming pool has eight lanes. How many ways can eight swimmers be assigned to these lanes for a race?
Feb 28­11:56 AM
December 07, 2010
Your final questions:
1. License plates in a certain state contain 7 positions. The first three
positions can have the numbers 0 ­ 9 in them. The last four positions
can contain the letters A ­ Z (26 letters). How many license plates can the state issue? 2. In a race there are 8 people. How many different ways can the 8 racers come in 1st, 2nd, and 3rd.
Feb 28­1:51 PM
Homework
Factorials and Counting Methods worksheet
Feb 28­2:11 PM
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