To determine the total number of combinations Duncan has to choose from, we use the fundamental counting principle:

Step-by-step explanation:

1. Duncan has 3 vehicle options:
   • station wagon, truck, or van.
2. The paint comes in 3 colors:
   • purple, red, or yellow.

Each vehicle can be paired with any of the paint colors. Therefore, the total number of combinations is calculated as: $\text{Total combinations} = (\text{number of vehicles}) \times (\text{number of colors})$ $\text{Total combinations} = 3 \times 3 = 9$

Final Answer:

Duncan has 9 combinations to choose from.

Do you want a detailed example of all possible combinations or clarification on any part? Let me know!

Related Questions:

1. What if Duncan has 4 vehicle options instead of 3? How many combinations would that make?
2. If a fourth paint color is added, how many combinations would there be now?
3. How would the answer change if Duncan could only choose between two vehicles?
4. What is the formula for combinations when there are multiple independent choices?
5. How can a tree diagram be used to visually show all combinations?

Tip: Always multiply the number of options for each category when choices are independent!