In State X, all vehicle license plates have 2 letters from the 26 lett

Take the task of creating as license plate and break it into stages.

Stage 1: Select the first character
This must be a letter from the alphabet.
So, we can complete stage 1 in 26 ways

Stage 2: Select the second character
This must be a letter from the alphabet.
Also, since repetitions are allowed, we can complete stage 2 in 26 ways

Stage 3: Select the third character
This must be a digit (0, 1, 2, 3, 4, 5, 6, 7, 8, or 9)
We can complete stage 3 in 10 ways

Stage 4: Select the fourth character
This must be a digit.
Since repetitions are allowed, we can complete stage 4 in 10 ways

Stage 5: Select the fifth character
This must be a digit.
Since repetitions are allowed, we can complete stage 5 in 10 ways

By the Fundamental Counting Principle (FCP), we can complete all 5 stages (and thus create a license plate) in (26)(26)(10)(10)(10) ways
Note, before we perform any calculations, we should recognize that (26)(26)(10)(10)(10) = (26)(26)(1000)
So, the answer must end in 000

Answer:

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

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