Be careful with your licence plates!

Discrete Mathematics Level 5

In Kansas, vehicle licence plates each have exactly three letters followed by three digits. We are told that to produce such a licence plate, it costs $\$n$ for each digit $n>0$ and $\$10$ for each digit $0$ . For letters, the cost is proportional to the position of the letter in the alphabet, namely, $\$1$ for $A$ , $\$2$ for $B$ and so on, up to $\$26$ for $Z$ .

Determine how many different licence plates would cost exactly $\$100$ .

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