2. Vocabulary Tree Diagram – A way for counting possible outcomes Sample Space – List of all possible outcomes Event – Any collection of one or more outcomes in the sample space Fundamental Counting Principle – If an event M can occur in m ways and is followed by an event N that can occur in n ways, then the event M followed by N can occur in m*n ways. Factorial – The expression n!, read n factorial, where n is greater than zero, is the product of all the positive integers beginning with n and counting backwards to 1

3. Tree Diagrams  We have 3 different ice creams and 3 different toppings to choose from, and can make 9 different sundaes

4. Tree Diagrams  Your Turn: Draw a tree diagram and find the number of outcomes. In ordering new t-shirts for school the students are given the following options: Maroon, White, or Black shirts; Short or Long sleeves; and the Mascot or ERHS in the corner

5. Fundamental Counting Principle  The Too Cheap computer company sells custom made personal computers. Customers have a choice of 11 different hard drives, 6 different keyboards, 4 different mice, and 4 different monitors. How many different custom computers can you order? Multiply to find the number of custom computers hard drive choices keyboard choices mice choices monitor choices number of custom computers 61 4410561056 11 * 6 * 4 * 4 = 1056 Answer: The number of different custom computers is 1056.

6. Fundamental Counting Principle  Your Turn: The local sub shop offers 5 types of subs, 9 types of sides, 6 types of beverages, and 3 desserts. How many different combos can you make? Solution: 810

7. Try it out  We need to break into groups of four.  Then try to discover in how many different ways your group can line up.  Start with by choosing one for the front, then for second, third, and last.  Then rearrange.  Continue until your group has the number

8. Counting Arrangements  Mr. Anderson is arranging 5 students into an seating arrangement of 5 desks, in how many ways can the students be arranged?  To solve this: - There are 5 students to choose from for the first desk - Then there are 4 students for the second - then 3 for the third, this continues till there is only one for the last. Let n represent the number of student:s n = 5*4*3*2*1 = 120 = 5! There are 120 ways to arrange the students

9. Counting Arrangements  Your Turn: The cheerleaders are doing a pyramid for the Friday pep rally, in how many ways can they fill the positions if the pyramid will use all the cheerleaders and there are 8 of them? Solution: 40,320