A1127CountingAndPermutations.notebook
November 18, 2014
Counting Methods and Permutations
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A1127CountingAndPermutations.notebook
November 18, 2014
You have 3 shirts and 2 pair of pants.
Make a tree diagram to find the number of outfits you have.
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A1127CountingAndPermutations.notebook
November 18, 2014
Multiplication Counting Principle
If there are m ways to make a first selection and n ways to make a second selection, there are m x n ways to make the two selections.
You have 4 shirts and 5 shorts.
On the map there are two tunnels for cars going from
New Jersy to Manhattan, NY, and three bridges from
Manhattan to Brooklyn, NY. How many routes using a tunnel and then a bridge are there from New Jersey to
Brooklyn through Manhattan?
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A1127CountingAndPermutations.notebook
November 18, 2014
An Arrangement of Items where ORDER IS IMPORTANT
How many ways can you arrange all three of the letters A, B, C when Order Is Important???
How many ways can you arrange two out of the four letters A, B, C, D when Order Is Important???
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A1127CountingAndPermutations.notebook
November 18, 2014
n P r n = how many things in the group.
r = how many of the things that you are picking at a time.
Start at the number n and use the first r numbers going toward zero.
How many ways can you pick 3 people out of 8 when order is important?
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A1127CountingAndPermutations.notebook
November 18, 2014
Special Permutations
How many ways can you line up everything in the group?
(Not just pick a few.)
Factorial (!)
How many different ways can you line up a group of 5 things?
(When order is important.)
5! = 5x4x3x2x1 = 120
5 P 5 = 5x4x3x2x1 = 120
Example:
How many different batting orders can you have with 9 baseball players?
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A1127CountingAndPermutations.notebook
November 18, 2014
You use six different letters to make a computer password.
Find the number of possible sixletter passwords.
It is a permutation calculation because Order is Important
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A1127CountingAndPermutations.notebook
November 18, 2014
Notes Continued on Next Page...
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