Question - Calculating Possible License Plate Combinations
mathotherlicense plate combinationscombinatorics problemprobability calculationletter and digit combinations
Solution:
The image provided contains a text that seems to refer to a combinatorics or probability problem involving license plates. Due to the resolution, I can't read the full text, but the part that is visible mentions that it is about license plates with three letters followed by three digits. The letters I and O are omitted, and the digits 1, 2, and 9 are not used. Since there are 24 letters (excluding I and O from the 26 letters of the English alphabet) and 7 usable digits (excluding 1, 2, and 9 from the 10 digits 0-9), we can calculate the number of possible license plates.For each position for the letters, there are 24 possibilities since two letters are omitted from the alphabet. For each position of the numbers, there are 7 possibilities since three numbers are omitted from the 0-9 range.The total number of different license plates that can be generated is calculated by multiplying the number of possibilities for each position:Number of letter combinations = 24 * 24 * 24 (because the letters can be repeated)Number of digit combinations = 7 * 7 * 7 (because the digits can be repeated)The total number of license plate combinations = Number of letter combinations * Number of digit combinationsLet's calculate this:Number of letter combinations = 24^3 = 13,824Number of digit combinations = 7^3 = 343Total combinations = 13,824 * 343 = 4,741,632So, there are 4,741,632 different possible license plates that can be generated using this format.
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