Question

suppose each license plate in a certain state has four letters followed by two digits. the letters i, o, q, and u and the digits 0, 1, 2, and 3 are not used. so, there are 22 letters and 6 digits that are used. assume that the letters and digits can be repeated. how many license plates can be generated using this format? license plates

Explanation:

Step1: Determine the number of choices for each letter position

Since there are 22 letters and repetition is allowed, for each of the four - letter positions, there are 22 choices. By the multiplication principle, the number of ways to choose the four letters is \(22\times22\times22\times22=22^{4}\).

Step2: Determine the number of choices for each digit position

Since there are 6 digits and repetition is allowed, for each of the two - digit positions, there are 6 choices. By the multiplication principle, the number of ways to choose the two digits is \(6\times6 = 6^{2}\).

Step3: Calculate the total number of license plates

Using the multiplication principle for the entire license - plate (letters and digits together), the total number of license plates is \(22^{4}\times6^{2}\).

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Answer:

\(8433216\)