The Counting Principle Uses multiplication to find the number of possible ways two or more events can occur.

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 or apple juice) and three choices of dessert (pie, ice cream, or jello). How many different meal combos can you select?_________ 12 meals Example 1: The Counting Principle

Method 2: Multiply Number of Choices (2 main courses, 2 drinks, & 3 desserts) 2 x 2 x 3 = 12 meals Example 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

8 Example 3: With Repetition License plates for cars are labeled with 3 letters followed by 3 digits. How many possible plates are there? You can use the same number more than once. xxxxx ___ x ___ x ___ x ___ x ___ x ___ = ,576,000 plates Example 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? xxxx ___ x ___ x ___ x ___ x ___ = 10 80,000 different account #’s

Ex5. Ten people are entered in a race. If there are no ties, in how many ways can the first three places come out? xx ___ x ___ x ___ = Ex6. How many different arrangements can be made with the letters in the word LUNCH? xxx ___ x ___ x ___ x ___ x ___ = Ex7. You and 8 friends go to a concert. How many different ways can you sit in the assigned seats? xxxxx= ___ x ___ x ___ x ___ x ___ x ___ x ___ x ___ = ,320

Example 8: Finding a Probability EMS is giving 5-digit identification numbers to students randomly. The first digit must not be 0. What is the probability that your ID # is 54321? Solution a)Find the total number of different ID#s. Use the Counting Principle. b) Then find the probability that your ID# is P (54321) = xxx ___ x ___ x ___ x ___ x ___ = ,000 10

Ex 9. You randomly choose a 7-digit code to open your garage door. What is the probability that you choose the code ? Ex 10. You flip a coin, roll a 6-sided number cube, and spin a spinner. The spinner is divided into 8 equal parts, labeled a, b, c, d, e, f, g, and h. Find the probability that you flip heads, roll an even number, and spin a vowel.