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2006 AMC 10A Problem 18

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2006 AMC 10A Problem 18AMC 10 Step by Step
Name:                             Date: September 13, 2026
Basic Counting · difficulty 3 of 5 · about 3 min · position P16-20

A license plate in a certain state consists of 44 digits, not necessarily distinct, and 22 letters, also not necessarily distinct. These six characters may appear in any order, except that the two letters must appear next to each other. How many distinct license plates are possible?

  1. A)

    104×26210^4\times 26^2

  2. B)

    103×26310^3\times 26^3

  3. C)

    5×104×2625\times 10^4\times 26^2

  4. D)

    102×26410^2\times 26^4

  5. E)

    5×103×2635\times 10^3\times 26^3

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