Let's analyze the image and solve the mathematical questions. The two questions are:

Question 6:

A new model of a car is available in six exterior colors, three interior colors, and two interior styles. How many versions of the car are available for order?
Options:

• A) 2
• B) 6
• C) 36
• D) 720

Solution:

To determine the total number of versions, we multiply the number of options for each category: $6 \text{ (exterior colors)} \times 3 \text{ (interior colors)} \times 2 \text{ (interior styles)} = 36$

Answer: C) 36

Question 7:

A multiple-choice test contains five questions, and each question has four options. In how many ways can the five questions be answered?
Options:

• A) 20
• B) 25
• C) 625
• D) 1,024

Solution:

Each question has 4 possible answers, and there are 5 questions. The total number of ways is: $4^5 = 4 \times 4 \times 4 \times 4 \times 4 = 1,024$

Answer: D) 1,024

Let me know if you need further details or have additional questions!

Relative Questions:

1. How can you calculate combinations for similar problems with different conditions?
2. What is the difference between permutations and combinations, and when to use each?
3. If the car had more options (e.g., 10 exterior colors), how would the total versions be calculated?
4. For the test problem, what would the result be if there were only three questions with the same options?
5. How do exponentiation principles apply to decision-making problems like these?

Tip: Always check if the problem requires ordering of items (permutations) or simply counts unique groupings (combinations).