Math Problem Statement
A person can order a new car with a choice of
1212
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?
Solution
To determine the total number of ways a new car can be ordered with regard to these options, we need to account for the number of choices for each feature.
Step 1: Analyze the options
- Color: 1212 choices.
- Air conditioning: 2 choices (with or without).
- Automatic transmission: 2 choices (with or without).
- Power windows: 2 choices (with or without).
- CD player: 2 choices (with or without).
Step 2: Multiply the choices
The total number of combinations is given by multiplying the choices for each feature:
Substitute the values:
Final Answer:
The car can be ordered in 19,392 different ways.
Would you like me to provide additional details or a breakdown of this solution?
Here are 5 related questions:
- What if the car manufacturer offered more or fewer colors? How would that change the calculation?
- How would the calculation change if additional features were added?
- What if some combinations (e.g., certain colors with specific options) were restricted?
- Can this method be generalized to other customizable products?
- How can we represent this problem using permutations or combinations?
Tip: When solving similar problems, clearly list all features and their options to avoid missing any combinations.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Combinatorics
Multiplication Principle
Formulas
Total combinations = (choices for color) × (choices for air conditioning) × (choices for automatic transmission) × (choices for power windows) × (choices for CD player)
Theorems
Multiplication Principle of Counting
Suitable Grade Level
Grades 8-10
Related Recommendation
Automobile Combinations: Styles, Engines, Transmissions, and Colors
Calculate Car and Paint Combinations Using the Counting Principle
Vehicle Probability Combinations at a Car Dealership
Calculate the Number of Ways to Select Cars and Trucks for a Safety Inspection
How to Calculate Total Car Versions and Multiple-Choice Test Answers