Question

a person can order a new car with a choice of 10 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.

Explanation:

Step1: Count the number of choices for each feature

• Color: 10 choices.
• Air - conditioning: 2 choices (with or without).
• Transmission: 2 choices (with or without automatic).
• Power windows: 2 choices (with or without).
• CD - player: 2 choices (with or without).

Step2: Apply the fundamental counting principle

The fundamental counting principle states that if there are \(m_1\) ways to do one thing, \(m_2\) ways to do a second thing, \(\cdots\), \(m_n\) ways to do an \(n\)th thing, then the total number of ways to do all \(n\) things together is \(m_1\times m_2\times\cdots\times m_n\).

Here, \(m_1 = 10\), \(m_2=2\), \(m_3 = 2\), \(m_4=2\), \(m_5=2\).

The total number of ways \(N=10\times2\times2\times2\times2\)

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Answer:

160