Problem 29
Question
The model of the car you are thinking of buying is available in nine different colors and three different styles (hatchback, sedan, or station wagon). In how many ways can you order the car?
Step-by-Step Solution
Verified Answer
There are 27 different ways to order a car considering the color and style options.
1Step 1: Identify Independent Choices
First, the problem gives two independent sets of choices. These are the different colors and styles of the car. There are 9 options for colors and 3 options for styles.
2Step 2: Apply the Fundamental Principle of Counting
According to the Fundamental Principle of Counting, if there are m ways for one event to occur and n ways for a second event to occur, then there are m*n ways for both events to occur.
3Step 3: Calculate total combination
The number of ways you can order the car by color and style would then be 9 (colors) * 3 (styles) = 27. So there are 27 different ways to order the car considering color and style options.
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