Problem

A person can order a new car with a choice of 6 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 different ways that a new car can be ordered.

Solution

Step 1 :This problem is about combinations. Each feature of the car can be considered as a binary choice (either you choose it or you don't). So, for each feature, there are 2 possibilities.

Step 2 :Since there are 6 colors and 5 binary features (air conditioning, automatic transmission, power windows, CD player), we can calculate the total number of combinations by multiplying the number of color choices by the number of combinations of features.

Step 3 :Using the formula for combinations, we get \(6 * 2^5\).

Step 4 :Calculating the above expression, we get 192.

Step 5 :Final Answer: The number of different ways a new car can be ordered with regard to these options is \(\boxed{192}\).

From Solvely APP
Source: https://solvelyapp.com/problems/29355/

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