SOLUTION: How many different license plates can be made using 4 letters followed by 3 digits selected from the digits 0 through 9, if digits may be repeated but letters may not be repeated?

Question 692372: How many different license plates can be made using 4 letters followed by 3 digits selected from the digits 0 through 9, if digits may be repeated but letters may not be repeated?
a) 358,800,000

b) 1,794,000

c) 258,336,000

d) 456,099

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
With a 26-letter alphabet, there are different choices for the first letter.
Each first letter choice leaves you other letters that can be chosen as second letter.
So there are ways to choose the first two letters,
and for each of those choices there are still other letters to choose the third letter from.
So there are ways to choose the first three letters,
and for each of those choices there are still other letters to choose the fourth letter from.
So there are ways to choose the four letters at the beginning of the license plate.
Then, there are 10 ways to choose each of the three digits, resulting in
combinations of three digits, from 000 to 999,
that can follow each of the allowed four-letter combinations.
That gives us possible different license plates.
So the correct answer is a).
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