The Fundamental Counting Principle states that if there are x ways to choose a first item and y ways to choose a second item, then there are x(y) ways to choose all items. FUNDAMENTAL COUNTING PRINCIPLE

A telephone company is assigned a new area code and can issue new 7- digit phone numbers. All phone numbers are equally likely. Find the number of possible 7-digit phone numbers Use the Fundamental Counting Principle: 1 st digit 2 nd digit 3 rd digit 4 th digit 5 th digit 6 th digit 7 th digit ?? ? ?? ? ? There are 10 choices for each digit (0-9), so there are 10(10)(10)(10)(10)(10)(10) = 10,000,000 phone number options FOR EXAMPLE

A telephone company is assigned a new area code and can issue new 7- digit phone numbers. All phone numbers are equally likely. Find the probability of a phone number that does not contain an 8. First, use the fundamental counting principle to find the number of phone numbers that do not contain an 8. 9(9)(9)(9)(9)(9)(9) = 4,782,969 P(no 8) = 4,782,969 = ,000,000 YOU TRY

The Fundamental Counting Principle tells you only the number of outcomes in some experiments, not what the outcomes are. A tree diagram is a way to show all possible outcomes. For example: A pizza place specializes in two types of crust, sesame and plain, and sells five different toppings, onions, olives, ham, green peppers, and mushrooms. Create a tree diagram to show the options assuming there is only one type of crust with one topping. USING A TREE DIAGRAM

Using the Fundamental Counting Principle, we know that we should have 10 options: 2 pizza crusts, 5 toppings…2(5)=10 TREE DIAGRAMS

You are going on a trip. You can pack 2 pairs of pants, 3 shirts, and 2 sweaters for your vacation. Use a tree diagram to show all outfit options you can make if each outfit consists of a pair of pants, a shirt, and a sweater. There are 12 total outfits to choose from 2(3)(2) = 12 YOU TRY

If one group contains x objects and a second group contains y objects, and the groups have no objects in common, then there are x + y options. For example How many items can you choose from Bergen’s Deli menu? None of the lists contains identical items, so use the Addition Counting Principle. Total Choices = Sandwiches + Salads + Soups T = There are 10 total items to choose from THE ADDITION COUNTING PRINCIPLE SandwichesSaladsSoups Turkey Ham Roast Beef Reuben Cobb Salad Taco Salad Grill Chicken Salad Tomato Chicken Noodle French Onion