1. Counting Principles and Permutations

2. Sample Space: set of all possible outcomes in an experiment A coin is tossed twice. Represent the sample space in a table and in a tree diagram. OutcomeHeadsTails Heads Tails OutcomesHeads Tails HeadsTails

3. Fundamental Counting Principle If there are m ways to make first selection and n ways to make a second selection, then there are m x n ways to make the two selections. Example: If you have 4 shirts and 3 pants then that would be 12 (4 x 3) outfit choices.

4. Permutations Permutation – is an arrangement of objects in a certain order. No item can be used more than once and order makes a difference. Permutation Notation – n is objects arranged r at a time. n P r =

5. Examples 1) At a local pizza shop, there are 4 vegetable toppings and 5 meat toppings. If you select one vegetable and one meat topping how many different possible pizzas are there?

6. Examples 2) At Wendy’s, when you purchase a combo, you have a choice of 9 sandwiches, 5 sides and 13 drinks. How many different meals are possible?

7. Examples Simplify the expression. 3) 9 P 3 4) 7 P 3 5) 5 P 2

8. Examples 6) There are 26 letters in the alphabet. For a password, you must use 5 letters. How many passwords are possible if letters cannot repeat?