Fundamental counting principle Fundamental Counting Principal = Fancy way of describing how one would determine the number of ways a sequence of events can take place. Fancy way of describing how one would determine the number of ways a sequence of events can take place.

Fundamental counting principle You are at your school cafeteria that allows you to choose a lunch meal from a set menu. You have two choices for the Main course (a hamburger or a pizza), Two choices of a drink (orange juice, apple juice) and Three choices of dessert (pie, ice cream, jello). How many different meal combos can you select?_________ Method one: Tree diagram Lunch HamburgerPizza AppleOrange Pie Icecream Jello 12 meals

Fundamental counting principle Method two: Multiply number of choices 2 x 2 x 3 = 12 meals Ex 2 : No repetition During the Olympic 400m sprint, there are 6 runners. How many possible ways are there to award first, second, and third places? 3 places____ x ____ x ____ = different ways 1st2nd3rd

Ex 3: With repetition License Plates for cars are labeled with 3 letters followed by 3 digits. (In this case, digits refer to digits If a question asks for numbers, its because 0 isn't really a number) How many possible plates are there? You can use the same number more than once. ___ x ___ x ___ x ___ x ___ x ___ = ,576,000 plates Ex 4: Account numbers for Century Oil Company consist of five digits. If the first digit cannot be a 0 or 1, how many account numbers are possible? ___ x ___ x ___ x ___ x ___ =810 80,000 different account #’s

5 Basic Counting Principles The product rule: Suppose that a procedure can be broken down into two successive tasks. If there are x ways to do the first task and y ways to do the second task after the first task has been done, then there are xy ways to do the procedure.

6 Basic Counting Principles Example: How many different license plates are there that containing exactly three English letters ? Solution: There are 26 possibilities to pick the first letter, then 26 possibilities for the second one, and 26 for the last one. So there are 26  26  26 = different license plates.

Example 1: Ken has 6 different pairs of slacks, 8 different shirts, 5 different pairs of shoes, and 3 different ties. How many outfits consisting of one pair of slacks, one shirt, one pair of shoes, and one tie can he create?

Example 2: At a veggie pizza stand, a pizza can be ordered with any combinations of 8 toppings: tomatoes, peppers, olives, pineapple, artichoke hearts, onion, jalapeño, and zucchini. How many different ways are there to order a pizza and toppings?

Example 3: An automobile license plate consists of three letters (A-Z) followed by three digits (0-9). How many different license plates are possible?

Example 4: An automobile license plate consists of three letters (A-Z) followed by three digits (0-9), but with no redundancies.