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Counting Outcomes

Counting Outcomes. 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

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Counting Outcomes

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  1. Counting Outcomes

  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*nways. 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. number ofcustom computers hard drive choices keyboardchoices micechoices monitorchoices 11 6 4 4 1056 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 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:sn = 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

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