pt) Anne, Bill, and Cathy are eating dinner together
at a restaurant. When it is time for dessert,
the server tells them that the restaurant has apple, cherry, pecan, blueberry, and pumpkin pies; carrot, German chocolate, coconut, and apple spice cakes; and vanilla, chocolate, strawberry, and spumoni ice cream.
The restaurant has an ample supply of each of these,
so each person can select a dessert without
concern for what the others may order.
In how many outcomes can 1 person have pie, 1 person have ice cream, and 1 perosn have cake?
728
363
384
192
To find the number of outcomes where one person has pie, one person has ice cream, and one person has cake, we can use the concept of the multiplication principle.
Step 1: Count the number of options for each person's dessert:
- For the person having pie, there are 5 options (apple, cherry, pecan, blueberry, pumpkin).
- For the person having ice cream, there are 4 options (vanilla, chocolate, strawberry, spumoni).
- For the person having cake, there are 4 options (carrot, German chocolate, coconut, apple spice).
Step 2: Multiply the number of options for each person together:
5 options for pie x 4 options for ice cream x 4 options for cake = 80 possible outcomes.
Therefore, there are 80 outcomes where one person has pie, one person has ice cream, and one person has cake.