SOLUTION: How many different license plates with repetition involving 3 letters and 4 digits if 3 letters must appear together at the beginning or at the end of plate.

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Question 1152872: How many different license plates with repetition involving 3 letters and 4 digits if 3 letters must appear together at the beginning or at the end of plate.
Found 2 solutions by greenestamps, rothauserc:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Number of sequences (permutations) of 3 letters with repetition (assuming the English language alphabet with 26 letters): 26*26*26 = 26^3

Number of permutations of 4 digits with repetition: 10^4

Number of permutations of the group of 3 letters and the group of 4 digits: 2

Number of license plates: (2)(26^3)(10^4)

Use a calculator if the answer is required in a simplified form.

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
There are 26 letters(A-Z) and 10 digits(0-9)
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Since letters can repeat, we have 26^3 permutations to form letters on the license plate
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Since the digits can repeat, we have 10^4 permutations to form digits on the license plate
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Since the letters can appear at the front or the back, we multiply by 2
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Therefore,
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There are 2 * 26^3 * 10^4 = 351,520,000 license plates
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