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Algebra 1 Predicting Patterns & Examining Experiments Unit 7: You Should Probably Change Section 4: Making Choices.

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Presentation on theme: "Algebra 1 Predicting Patterns & Examining Experiments Unit 7: You Should Probably Change Section 4: Making Choices."— Presentation transcript:

1 Algebra 1 Predicting Patterns & Examining Experiments Unit 7: You Should Probably Change Section 4: Making Choices

2 How many ways could the class choose a committee of four students? Student Question #5...

3 How many ways could the class choose a committee of four students? If the class had four students, there is only one way to choose four for a committee. But our class has eleven.... How many ways could the class choose a committee of four students? If the class had four students, there is only one way to choose four for a committee. But our class has eleven.... Student Question #5... These are all the same committee: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA These are all the same committee: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA

4 How many ways could the class choose a committee of four students? Out of eleven students, we can arrange four students 7920 ways. How many ways could the class choose a committee of four students? Out of eleven students, we can arrange four students 7920 ways. Student Question #5... But....

5 How many ways could the class choose a committee of four students? Out of eleven students, we can arrange four students 7920 ways, but we are not arranging them (just choosing them). So, the 24 arrangements for each group needs to be removed. How many ways could the class choose a committee of four students? Out of eleven students, we can arrange four students 7920 ways, but we are not arranging them (just choosing them). So, the 24 arrangements for each group needs to be removed. Student Question #5...

6 How many ways could the class choose a committee of four students? Out of eleven students, we can CHOOSE four students 330 different ways. How many ways could the class choose a committee of four students? Out of eleven students, we can CHOOSE four students 330 different ways. Student Question #5...

7 Combination Notation

8 A combination is a choosing of objects NOT in a specific order. Combinations Defined

9 A combination is a choosing of objects NOT in a specific order. Combinations Defined

10 How many ways could the class choose a committee of four students? Out of eleven students, we can CHOOSE four students 330 different ways: How many ways could the class choose a committee of four students? Out of eleven students, we can CHOOSE four students 330 different ways: Student Question #5...

11 How many hands? How many different 5- card hands can be dealt out of a 52-card deck?

12 How many hands?

13 How many different 5- card hands can be dealt out of a 52-card deck? There are almost 2.6 million different hands. How many different 5- card hands can be dealt out of a 52-card deck? There are almost 2.6 million different hands. How many hands?

14 At a local juice store, you can mix and match ingredients to create your own smoothie. From nine juices you can choose three, from five sherbets you can choose two, and from eight vitamin powders you can choose one. How many different smoothies can be made? At a local juice store, you can mix and match ingredients to create your own smoothie. From nine juices you can choose three, from five sherbets you can choose two, and from eight vitamin powders you can choose one. How many different smoothies can be made? How many smoothies?

15 At a local juice store, you can mix and match ingredients to create your own smoothie. From nine juices you can choose three, from five sherbets you can choose two, and from eight vitamin powders you can choose one. How many different smoothies can be made? At a local juice store, you can mix and match ingredients to create your own smoothie. From nine juices you can choose three, from five sherbets you can choose two, and from eight vitamin powders you can choose one. How many different smoothies can be made? How many smoothies? Choices Juices: Sherberts: Powders: Choices Juices: Sherberts: Powders:

16 At a local juice store, you can mix and match ingredients to create your own smoothie. From nine juices you can choose three, from five sherbets you can choose two, and from eight vitamin powders you can choose one. How many different smoothies can be made? At a local juice store, you can mix and match ingredients to create your own smoothie. From nine juices you can choose three, from five sherbets you can choose two, and from eight vitamin powders you can choose one. How many different smoothies can be made? How many smoothies? Choices Juices: Sherberts: Powders: Choices Juices: Sherberts: Powders:

17 At a local juice store, you can mix and match ingredients to create your own smoothie. From nine juices you can choose three, from five sherbets you can choose two, and from eight vitamin powders you can choose one. How many different smoothies can be made? At a local juice store, you can mix and match ingredients to create your own smoothie. From nine juices you can choose three, from five sherbets you can choose two, and from eight vitamin powders you can choose one. How many different smoothies can be made? How many smoothies? Choices Juices: Sherberts: Powders: Choices Juices: Sherberts: Powders:

18 At a local juice store, you can mix and match ingredients to create your own smoothie. From nine juices you can choose three, from five sherbets you can choose two, and from eight vitamin powders you can choose one. How many different smoothies can be made? At a local juice store, you can mix and match ingredients to create your own smoothie. From nine juices you can choose three, from five sherbets you can choose two, and from eight vitamin powders you can choose one. How many different smoothies can be made? How many smoothies? Choices Juices: Sherberts: Powders: Choices Juices: Sherberts: Powders:

19 At a local juice store, you can mix and match ingredients to create your own smoothie. From nine juices you can choose three, from five sherbets you can choose two, and from eight vitamin powders you can choose one. How many different smoothies can be made? At a local juice store, you can mix and match ingredients to create your own smoothie. From nine juices you can choose three, from five sherbets you can choose two, and from eight vitamin powders you can choose one. How many different smoothies can be made? How many smoothies? Choices Juices: Sherberts: Powders: Choices Juices: Sherberts: Powders:

20 At a local juice store, you can mix and match ingredients to create your own smoothie. From nine juices you can choose three, from five sherbets you can choose two, and from eight vitamin powders you can choose one. How many different smoothies can be made? At a local juice store, you can mix and match ingredients to create your own smoothie. From nine juices you can choose three, from five sherbets you can choose two, and from eight vitamin powders you can choose one. How many different smoothies can be made? How many smoothies? Choices Juices: Sherberts: Powders: Choices Juices: Sherberts: Powders:

21 At a local juice store, you can mix and match ingredients to create your own smoothie. From nine juices you can choose three, from five sherbets you can choose two, and from eight vitamin powders you can choose one. How many different smoothies can be made? At a local juice store, you can mix and match ingredients to create your own smoothie. From nine juices you can choose three, from five sherbets you can choose two, and from eight vitamin powders you can choose one. How many different smoothies can be made? How many smoothies? Choices Juices: Sherberts: Powders: Choices Juices: Sherberts: Powders:

22 At a local juice store, you can mix and match ingredients to create your own smoothie. From nine juices you can choose three, from five sherbets you can choose two, and from eight vitamin powders you can choose one. How many different smoothies can be made? At a local juice store, you can mix and match ingredients to create your own smoothie. From nine juices you can choose three, from five sherbets you can choose two, and from eight vitamin powders you can choose one. How many different smoothies can be made? How many smoothies? Choices = 84 10 8 Juices: Sherberts: Powders: Choices = 84 10 8 Juices: Sherberts: Powders:

23 At a local juice store, you can mix and match ingredients to create your own smoothie. From nine juices you can choose three, from five sherbets you can choose two, and from eight vitamin powders you can choose one. How many different smoothies can be made? At a local juice store, you can mix and match ingredients to create your own smoothie. From nine juices you can choose three, from five sherbets you can choose two, and from eight vitamin powders you can choose one. How many different smoothies can be made? How many smoothies? Choices = 84 10 8 = 6720 Juices: Sherberts: Powders: Choices = 84 10 8 = 6720 Juices: Sherberts: Powders:

24 At a local juice store, you can mix and match ingredients to create your own smoothie. From nine juices you can choose three, from five sherbets you can choose two, and from eight vitamin powders you can choose one. How many different smoothies can be made? At a local juice store, you can mix and match ingredients to create your own smoothie. From nine juices you can choose three, from five sherbets you can choose two, and from eight vitamin powders you can choose one. How many different smoothies can be made? How many smoothies? Choices = 84 10 8 = 6720 There are 6720 different smoothies that can be made at the juice store. Choices = 84 10 8 = 6720 There are 6720 different smoothies that can be made at the juice store.

25 If you randomly grab five skittles, what is the probability that you will pick exactly 3 green and 2 yellow candies? Probability of a Limon

26 If you randomly grab five skittles, what is the probability that you will pick exactly 3 green and 2 yellow candies? Facts: - There are 40 skittles in the bowl. - There are equal numbers of each of the five colors. If you randomly grab five skittles, what is the probability that you will pick exactly 3 green and 2 yellow candies? Facts: - There are 40 skittles in the bowl. - There are equal numbers of each of the five colors. Probability of a Limon

27 If you randomly grab five skittles, what is the probability that you will pick exactly 3 green and 2 yellow candies? There are 8 of each color, so: the number of ways to choose 3 greens: If you randomly grab five skittles, what is the probability that you will pick exactly 3 green and 2 yellow candies? There are 8 of each color, so: the number of ways to choose 3 greens: Probability of a Limon

28 If you randomly grab five skittles, what is the probability that you will pick exactly 3 green and 2 yellow candies? There are 8 of each color, so: the number of ways to choose 2 yellows: If you randomly grab five skittles, what is the probability that you will pick exactly 3 green and 2 yellow candies? There are 8 of each color, so: the number of ways to choose 2 yellows: Probability of a Limon

29 If you randomly grab five skittles, what is the probability that you will pick exactly 3 green and 2 yellow candies? There are 40 skittles, so: the number of ways to choose 5 candies: If you randomly grab five skittles, what is the probability that you will pick exactly 3 green and 2 yellow candies? There are 40 skittles, so: the number of ways to choose 5 candies: Probability of a Limon

30 If you randomly grab five skittles, what is the probability that you will pick exactly 3 green and 2 yellow candies? Probability = If you randomly grab five skittles, what is the probability that you will pick exactly 3 green and 2 yellow candies? Probability = Probability of a Limon

31 If you randomly grab five skittles, what is the probability that you will pick exactly 3 green and 2 yellow candies? Probability = If you randomly grab five skittles, what is the probability that you will pick exactly 3 green and 2 yellow candies? Probability = Probability of a Limon

32 If you randomly grab five skittles, what is the probability that you will pick exactly 3 green and 2 yellow candies? Probability = If you randomly grab five skittles, what is the probability that you will pick exactly 3 green and 2 yellow candies? Probability = Probability of a Limon

33 If you randomly grab five skittles, what is the probability that you will pick exactly 3 green and 2 yellow candies? Probability = If you randomly grab five skittles, what is the probability that you will pick exactly 3 green and 2 yellow candies? Probability = Probability of a Limon

34 If you randomly grab five skittles, what is the probability that you will pick exactly 3 green and 2 yellow candies? Probability = There is a.24% chance of picking exactly 3 green and 2 yellow candies. If you randomly grab five skittles, what is the probability that you will pick exactly 3 green and 2 yellow candies? Probability = There is a.24% chance of picking exactly 3 green and 2 yellow candies. Probability of a Limon

35 Disclaimer All photos contained are used under creative commons rights. 6 degrees of cards http://www.flickr.com/photos/insightimaging/3899220362/ Fresh fruit juice http://www.flickr.com/photos/blandm/3582158037/ Skittles http://www.flickr.com/photos/ambiebambie39507/2377420546/

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