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2006 AMC 10A Question 18

AMC10 · 2006 AMC 10A

Question 18

A license plate in a certain state consists of $4$ digits, not necessarily distinct, and $2$ 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. $10^4 \cdot 26^2$
  2. $10^3 \cdot 26^3$
  3. $5 \cdot 10^4 \cdot 26^2$
  4. $10^2 \cdot 26^4$
  5. $5 \cdot 10^3 \cdot 26^3$