I would think it would be $26\cdot26$ (for the two letters) and then for the digits it would be $10\cdot10\cdot10\cdot10$, so in total $26^2\cdot10^4=6760000$.
I don't know but I feel like im missing out on something.
2026-04-21 00:04:00.1776729840
Plates have the pattern LLDDDD; that is, two letters then four digits. How many distinct registration plates are possible with this system?
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Your solution is perfectly fine - on a license plate with a pattern $LLDDDD$ you can choose 1 letter out of 26 twice $(26\cdot 26=26^2)$ and 1 digit out of 10 quadruple $(10\cdot 10\cdot 10\cdot 10=10^4)$. Then, by combining all possibilities you get $26^2\cdot10^4=6760000$ various combinations.