1. Fundamental Counting Theorm

2. Fundamental Counting Principle Fundamental Counting Principle can be used determine the number of possible outcomes when there are two or more characteristics. Fundamental Counting Principle states that if an event has m possible outcomes and another independent event has n possible outcomes, then there are m * n possible outcomes for the two events together.

3. Fundamental Counting Principle Lets start with a simple example. A student is to roll a die and flip a coin. How many possible outcomes will there be? 1H 2H 3H 4H 5H 6H 1T 2T 3T 4T 5T 6T 12 outcomes 6*2 = 12 outcomes

4. Fundamental Counting Principle For a college interview, Robert has to choose what to wear from the following: 4 slacks, 3 shirts, 2 shoes and 5 ties. How many possible outfits does he have to choose from? 4*3*2*5 = 120 outfits

5. Now you try! 1. A restaurant offers four sizes of pizza, two types of crust, and eight toppings. How many possible combinations of pizza with one topping are there? 2. Rob has 4 shirts, 3 pairs of pants, and 2 pairs of shoes that all coordinate. How many outfits can you put together? 3. Grace loves to eat salad! How many salads can she put together if she can pick out one type of lettuce from 2 choices, one vegetable from 4 choices and one dressing from 7 choices? 4. How many 5-digit numbers can be formed (using 0 – 9)? 5. How many 5-digit numbers can be formed if each one uses all the digits 0, 1, 2, 3, 4 without repetition? 64 pizzas 24 outfits 56 salads 100,000 numbers 120 numbers

6. Closure  In how many ways can 6 bicycles be parked in a row? 720 ways