Suppose each license plate in a certain state has two digits, followed by two letters, followed by two digits. The letters Q and U are not used. So, there are 24 letters and 10 digits that are used. Assume that the letters and digits can be repeated. How many license plates can be generated using this format?licenseplates
Question
Suppose each license plate in a certain state has two digits, followed by two letters, followed by two digits. The letters Q and U are not used. So, there are 24 letters and 10 digits that are used. Assume that the letters and digits can be repeated. How many license plates can be generated using this format?licenseplates
Solution
To calculate the total number of possible license plates, we need to consider that each position in the license plate can be filled independently.
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For the first two positions, we have 10 choices (digits from 0 to 9) for each position. So, the total possibilities for the first two positions are 10 * 10 = 100.
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For the next two positions, we have 24 choices (letters from A to Z, excluding Q and U) for each position. So, the total possibilities for these two positions are 24 * 24 = 576.
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For the last two positions, again we have 10 choices (digits from 0 to 9) for each position. So, the total possibilities for the last two positions are 10 * 10 = 100.
To get the total number of possible license plates, we multiply the possibilities for each position together: 100 * 576 * 100 = 5,760,000.
So, there are 5,760,000 different license plates that can be generated using this format.
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