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Algebra 1 Notes: Probability Part 2: Counting Outcomes
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Objectives Calculate the number of possible outcomes using the fundamental counting principle
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Take A Guess How many different ways can I line up 8 students for a picture?
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Example 1 At football games, a student concession stand sells sandwiches on either wheat or rye bread. The sandwiches come with salami, turkey or ham; and either chips, a brownie, or fruit. Use a tree diagram to determine the number of possible sandwich combinations.
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Example 1 At football games, a student concession stand sells sandwiches on either wheat or rye bread. The sandwiches come with salami, turkey or ham; and either chips, a brownie, or fruit. Use a tree diagram to determine the number of possible sandwich combinations.
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Example 1 Bread
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Example 1 Bread wheat rye
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Example 1 BreadMeat wheat rye
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Example 1 At football games, a student concession stand sells sandwiches on either wheat or rye bread. The sandwiches come with salami, turkey or ham; and either chips, a brownie, or fruit. Use a tree diagram to determine the number of possible sandwich combinations.
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Example 1 At football games, a student concession stand sells sandwiches on either wheat or rye bread. The sandwiches come with salami, turkey or ham; and either chips, a brownie, or fruit. Use a tree diagram to determine the number of possible sandwich combinations.
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Example 1 BreadMeat salami wheat turkey ham rye
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Example 1 BreadMeat salami wheat turkey ham salami ryeturkey ham
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Example 1 BreadMeatSide Item salami wheat turkey ham salami ryeturkey ham
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Example 1 At football games, a student concession stand sells sandwiches on either wheat or rye bread. The sandwiches come with salami, turkey or ham; and either chips, a brownie, or fruit. Use a tree diagram to determine the number of possible sandwich combinations.
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Example 1 At football games, a student concession stand sells sandwiches on either wheat or rye bread. The sandwiches come with salami, turkey or ham; and either chips, a brownie, or fruit. Use a tree diagram to determine the number of possible sandwich combinations.
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Example 1 BreadMeatSide Item chips salamibrownie fruit wheatturkey ham salami ryeturkey ham
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Example 1 BreadMeatSide ItemOutcomes chips 1 salamibrownie 2 fruit 3 wheatturkey ham salami ryeturkey ham
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Fundamental Counting Principle Multiply the number of ways EACH event can occur.
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Example 1 At football games, a student concession stand sells sandwiches on either wheat or rye bread. The sandwiches come with salami, turkey or ham; and either chips, a brownie, or fruit. Use a tree diagram to determine the number of possible sandwich combinations.
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BreadsMeatSideTotal 2x 3 x 3 =
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BreadsMeatSideTotal 2x 3 x 3 = 18
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Example 2 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? hard drive choices 11
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Example 2 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? hard drivekeyboard choices choices 11
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Example 2 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? hard drivekeyboard choices choices 11 6
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Example 2 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? hard drivekeyboardmouse choices choiceschoices 11 6
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Example 2 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? hard drivekeyboardmouse choices choiceschoices 11 6 4
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Example 2 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? hard drivekeyboardmousemonitor choices choiceschoiceschoices 11 6 4
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Example 2 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? hard drivekeyboardmousemonitor choices choiceschoiceschoices 11 6 4 4
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Example 2 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? hard drivekeyboardmousemonitor choices choiceschoiceschoices 11 6 4 4
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Example 2 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? hard drivekeyboardmousemonitor choices choiceschoiceschoices 11 6 4 4 = 1,056
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Example 2 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? hard drivekeyboardmousemonitor choices choiceschoiceschoices 11 6 4 4 = 1,056 different computers
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Vocabulary Factorial – A number multiplied by every positive integer less than itself Looks like an exclamation point.
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Example 3 There are 8 students in the Biology Club at Central High School. The students want to stand in line for their yearbook picture. How many different ways could the 8 students stand for their picture?
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Example 3 There are 8 students in the Biology Club at Central High School. The students want to stand in line for their yearbook picture. How many different ways could the 8 students stand for their picture? 8 7 6 5 4 3 2 1
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Example 3 There are 8 students in the Biology Club at Central High School. The students want to stand in line for their yearbook picture. How many different ways could the 8 students stand for their picture? 8 7 6 5 4 3 2 1 = 8!
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Example 3 There are 8 students in the Biology Club at Central High School. The students want to stand in line for their yearbook picture. How many different ways could the 8 students stand for their picture? 8 7 6 5 4 3 2 1 = 8! = 40,320 40,320 ways they could stand
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Homework Worksheet: Counting Outcomes
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