There are a total of 10 digits (0-9) that can be used for the first three positions on the license plate.
Once a digit is used, it cannot be used again in the same plate.
There are a total of 26 letters (A-Z) that can be used for the last three positions on the license plate.
Similarly, once a letter is used, it cannot be used again in the same plate.
To calculate the total number of different license plates that can be formed, we can use the concept of permutations.
The number of ways to select and arrange 3 different digits from a set of 10 without repetition is given by:
10P3 = 10! / (10-3)! = 10! / 7! = 10 x 9 x 8 = 720
Similarly, the number of ways to select and arrange 3 different letters from a set of 26 without repetition is given by:
26P3 = 26! / (26-3)! = 26! / 23! = 26 x 25 x 24 = 15,600
To find the number of different license plates that can be formed, we will multiply these two values together:
720 x 15,600 = 11,232,000
Therefore, there are 11,232,000 different license plates that can be formed if each plate has 3 different digits followed by 3 different letters.
how many different license plates can be formed if each plate has 3 different digits followed by 3 different letters?*
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