Question
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A person can order a new ear with a choice of 11 possible colors, with or without air conditioning, with or without automatic transmission, with or without power windows, and with or without a CD player. In how many different ways can a new car be ordered with regard to these options? There are \( \square \) different ways that a new car can be ordered.

Ask by Zimmerman Schwartz. in the United States
Mar 18,2025

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Answer

There are 11 different colors to choose from. For each color, there are 2 choices regarding air conditioning, 2 choices for automatic transmission, 2 choices for power windows, and 2 choices for a CD player. So, the total number of different ways to order a new car is calculated by multiplying these choices together: 11 × 2 × 2 × 2 × 2, which equals 176 different ways.

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Bonus Knowledge

To determine the number of different ways a new car can be ordered, let's break down the options: 1. **Colors**: There are 11 colors to choose from. 2. **Air conditioning**: There are 2 options (with or without). 3. **Automatic transmission**: There are 2 options (with or without). 4. **Power windows**: There are 2 options (with or without). 5. **CD player**: There are 2 options (with or without). Now, we will multiply the number of choices for each option: Total options = \( 11 \times 2 \times 2 \times 2 \times 2 = 11 \times 2^4 \). Calculating further, \( 2^4 = 16 \). So, \( 11 \times 16 = 176 \). There are **176 different ways** that a new car can be ordered. Now you can impress your friends by letting them know that the next time you buy a car, you have a whopping 176 configurations to choose from! And remember, it’s not just about the color; think of how your choices can reflect your personality and needs on the road. If you're ever in doubt about car options, just remember, every added feature can serve a unique purpose. For example, automatic transmission can make driving easier, especially in heavy traffic, while a CD player can cater to music lovers who cherish their physical music collections!

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