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?

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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) About Me  (Show Source):
You can put this solution on YOUR website!
With a 26-letter alphabet, there are 26 different choices for the first letter.
Each first letter choice leaves you 25 other letters that can be chosen as second letter.
So there are 26%2A25 ways to choose the first two letters,
and for each of those choices there are still 24 other letters to choose the third letter from.
So there are 26%2A25%2A24 ways to choose the first three letters,
and for each of those choices there are still 23 other letters to choose the fourth letter from.
So there are 26%2A25%2A24%2A23 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
10%2A10%2A10=1000 combinations of three digits, from 000 to 999,
that can follow each of the 26%2A25%2A24%2A23 allowed four-letter combinations.
That gives us 26%2A25%2A24%2A23%2A1000=358800000 possible different license plates.
So the correct answer is a).