Provide an appropriate response.
-License plates are made using 3 letters followed by 3 digits. How many plates can be made if repetition of letters and digits is allowed?
A) 308,915,776
B) 1,757,600
C) 1,000,000
D) 175,760
E) 17,576,000

Question

Quizplus · Accepted Answer

There are 26 choices for each of the three letters (with repetition allowed) and 10 choices for each of the three digits (with repetition allowed). Therefore, the total number of possible license plates is 26^3 * 10^3 = 17,576,000. There are 26 letters and 10 digits that can be used for each spot on the license plate. Therefore, there are 26 x 26 x 26 possible letter combinations and 10 x 10 x 10 possible digit combinations. To find the total number of possible license plates, we multiply the two possibilities: 26 x 26 x 26 x 10 x 10 x 10 = 17,576,000. Therefore, the best choice is E.

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