A112­7CountingAndPermutations.notebook
January 07, 2013
Algebra 1
Ch.12 Notes Page 42
P42 12­7 Counting Methods and Permutations
Tree Diagrams
You have 3 shirts and 2 pair of pants.
Make a tree diagram to find the number of outfits you have.
Shirts
Pants
Outfits
A112­7CountingAndPermutations.notebook
January 07, 2013
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.
Examples:
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?
Permutations
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???
A112­7CountingAndPermutations.notebook
January 07, 2013
Permutation Calculation
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?
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?
A112­7CountingAndPermutations.notebook
January 07, 2013
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