Counting Outcomes

1
Chapter 14

• Counting Outcomes
• Fundamental Counting Principle
• Combinations Permutations

2
Counting Outcomes

• A sandwich shop uses either wheat or white bread.
  For a one topping sandwich, you can choose either
  ham, turkey, or roast beef. The cheese choice is
  either American or Swiss. Use a tree diagram to
  determine the number of possible one topping
  sandwiches.

3
Fundamental Counting Principle

• A home building company is in charge of building
  all of the homes for a new subdivision. They
  offer 6 different floor plans, a basement or no
  basement and 11 different exterior colors. How
  many different homes can you choose from?

4
Determine of Arrangements or of Orders

• Kayla is in charge of a talent show at her
  school. There are 8 contestants. She must choose
  in what order they will appear. How many
  different ways can she schedule the performers?

5
Permutations

• When order matters

nPr
n number of objects r number of choices of
objects
6
Permutation Example

• Race with 8 contestants, 4 placed. What are the
  total of possible outcomes?

nPr
8P4
1680 possible outcomes
7
Permutation Probability

• Contest with 8 people, 5 female, 3 male. What is
  the probability that the 4 placements will be
  female?
• P (1st, 2nd, 3rd, and 4th are female)

or about 7.14
8
Combinations

• When order is not important

nCr
n number of objects r number of choices of
objects
9
Combination Example

• Class of 30, choose 5 to be on group project.

nCr
30C5
142,506 possible combinations