My book says that if a license plate must have 3 letters, and 4 numbers, when repetition is allowed, and no restriction is placed on the order of letters and numbers, then the amount of possible license plates is:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\begin{pmatrix}7 \\3\end{pmatrix}10^{4}26^{3}[/tex]

[tex]\begin{pmatrix}7 \\3\end{pmatrix}[/tex] ways of permuting the letters and numbers, seems reasonable when all the letters and numbers are the same, such as:

AAA1111

But shouldn't there be7!possible unique permutations when they're all different, such as in say:

ABC1234

Thanks!

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# Number of different license plates

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