A new model of car is available in 4 exterior colors and 3 interior colors. Use a tree diagram and specific colors to show how many color schemes are possible for the car. Solve the problem using an alternative method as well.Note that you are asked to solve the problem in two different ways.
This site has several examples of tree diagrams.
http://www.enchantedlearning.com/graphicorganizers/tree/
10
To solve the problem using a tree diagram, we can draw a diagram with two branches representing the exterior and interior colors. The first branch will have 4 options for the exterior colors (let's say red, blue, white, and black), and the second branch will have 3 options for the interior colors (let's say beige, gray, and black).
Here's a possible tree diagram:
Exterior Colors:
- Red
- Beige
- Gray
- Black
- Blue
- Beige
- Gray
- Black
- White
- Beige
- Gray
- Black
- Black
- Beige
- Gray
- Black
To find the number of color schemes, we simply count the number of leaf nodes in the tree diagram. In this case, there are 4 exterior colors and 3 interior colors, so there are a total of 4 x 3 = 12 possible color schemes for the car.
Alternatively, we can use the multiplication rule to solve the problem.
The multiplication rule states that if there are n choices for one event and m choices for another event, then there are n x m total possibilities for both events combined.
In this case, there are 4 options for the exterior color and 3 options for the interior color. Therefore, there are 4 x 3 = 12 possible color schemes for the car.