Geometry

Question Analysis
This question involves a two - part permutation problem, one for the letters and one for the digits.
The main focus is on applying the permutation formula separately for the letters and digits and then using the multiplication principle to find the total number of license plates.

Key Concept Explanation
The multiplication principle states that if there are ways to do one thing and ways to do another thing, then there are ways to do both things.
For permutations of distinct objects, the formula gives the number of ways to arrange objects out of distinct objects.
Here, we have 26 letters in the alphabet () for the letter part of the license plate and 10 digits () for the digit part, and in both cases, as we are choosing 3 non - repeating characters.

Step - by - Step Solution
Calculate the number of ways to choose and arrange the 3 non - repeating letters:
Using the permutation formula with and , we have .
Since ,

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