Your plate numbers will be like
[tex] xxxyyy [/tex]
where each [tex] x [/tex] is a number, and each [tex] y [/tex] is a letter. Assuming you can use all numbers and letters, you have 10 possible choices for every [tex] x [/tex] place (all the digits from 0 to 10) and 26 possible choices for every [tex] y [/tex] place (all the letters from a to z).
So, if you multiply all the possible choices, you have
[tex] xxxyyy \to 10\cdot 10 \cdot 10 \cdot 26 \cdot 26 \cdot 26 = 10^3 \cdot 26^3 = (10\cdot 26)^3 = 260^3[/tex]
So, there is a total of
[tex] 260^3 = 17,576,000 [/tex]
possible plate numbers with 3 letters and 3 numbers, if repetitions are allowed.
