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Exploring Dinner Choices: Appetizers, Entrées, and Desserts with Tree Diagrams

Discover how to create three-course dinner combinations using the available menu options of appetizers, entrées, and desserts. This guide includes a visual tree diagram to illustrate possible meal pairings, enabling you to see different combinations. We apply the Fundamental Counting Principle to calculate the total number of outcomes without drawing the entire diagram. For example, if there are options for soup, steak, chicken, and desserts like carrot cake and apple pie, find out how to count the combinations efficiently.

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Exploring Dinner Choices: Appetizers, Entrées, and Desserts with Tree Diagrams

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Presentation Transcript

  1. Bell Work Three-course dinners can be made from the menu shown. Find the sample space for a dinner consisting of an appetizer, entrée, and dessert. Hint: Draw a tree diagram

  2. Bell Work Sample Space Soup, Steak, Carrot Cake Carrot Cake Steak Soup, Steak, Apple Pie Apple Pie Carrot Cake Soup, Chicken, Carrot Cake Chicken Soup Apple Pie Soup, Chicken, Apple Pie Carrot Cake Fish Soup, Fish, Carrot Cake Apple Pie Soup, Fish, Apple Pie Carrot Cake Salad, Steak, Carrot Cake Steak Apple Pie Salad, Steak, Apple Pie Carrot Cake Salad, Chicken, Carrot Cake Salad Chicken Apple Pie Salad, Chicken, Apple Pie Carrot Cake Salad, Fish, Carrot Cake Fish Apple Pie Salad, Fish, Apple Pie

  3. Counting Outcomes

  4. Counting Outcomes • The Fundamental Counting Principle allows you to calculate the number of possible outcomes without creating a tree diagram and counting the possible outcomes in the sample space.

  5. Counting Outcomes

  6. Counting Outcomes

  7. Let’s look back at the bell work… Sample Space Soup, Steak, Carrot Cake Salad, Steak, Carrot Cake Soup, Steak, Apple Pie Salad, Steak, Apple Pie Soup, Chicken, Carrot Cake Salad, Chicken, Carrot Cake Soup, Chicken, Apple Pie Salad, Chicken, Apple Pie Soup, Fish, Carrot Cake Salad, Fish, Carrot Cake Soup, Fish, Apple Pie Soup, Fish, Apple Pie 12 How many options did you find when you did the tree diagram? Let’s use the fundamental counting principle. 2 x 3 x 2 = 12

  8. Counting Outcomes ✔Check Your Progress Find the total number of outcomes when choosing from bike helmets that come in three colors and two styles. 6

  9. 60; 1/60; unlikely ✔Check Your Progress If the Jeans Shop adds relaxed fit jeans to its selection, find the number of available jeans. Then find the probability of randomly selecting a 36 x 30 relaxed fit pair of jeans. Is it likely or unlikely that the size would be chosen?

  10. ✔Check Your UnderstandingRally Coach 4 x 3 = 12 20 x 7 = 140 12 x 7 = 84 3 x 4 = 12 6 x 2 x 2 = 24 4 x 2 x 2 = 16

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