Question

each license plate in a certain state has six characters (with repeats allowed). here are the possibilities for each character. how many license plates are possible in this state?

Explanation:

Step1: Apply the counting principle

The counting principle states that if there are \(m_1\) ways to do the first task, \(m_2\) ways to do the second task, \(\cdots\), \(m_n\) ways to do the \(n\)th task, then the total number of ways to do all \(n\) tasks together is \(m_1\times m_2\times\cdots\times m_n\).
For the first three characters (letters), each has \(26\) possibilities. For the last three characters (digits), each has \(10\) possibilities.

Step2: Calculate the total number of license - plates

The total number of license plates \(N = 26\times26\times26\times10\times10\times10\).
We know that \(26\times26\times26=26^{3}\) and \(10\times10\times10 = 10^{3}\).

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Answer:

\(17576000\)