Final answer:
Using the multiplication principle, the auto manufacturer can produce 2,520 different varieties of cars by multiplying the number of choices for each category: 9 models, 8 colors, 7 upholstery fabrics, and 5 interior colors.
Step-by-step explanation:
To calculate how many different varieties of car an auto manufacturer can produce given 9 models, 8 different colors, 7 different upholstery fabrics, and 5 interior colors, we can use the multiplication principle of counting, also known as the fundamental counting principle. This principle states that if one event can happen in m ways and another independent event can happen in n ways, then there are m × n ways for both events to happen.
In this case, we have several independent choices that multiply together. The number of car varieties is the product of the number of options for each category. Therefore, the manufacturer can produce 9 (models) × 8 (colors) × 7 (upholsteries) × 5 (interior colors) = 2520 different varieties of car.