How many automobile license plates can be made, if each plate contains two different letters followed by three different digits ?

Explanation

To find the total number of automobile license plates that can be made with the specified conditions (two different letters followed by three different digits), we can break the problem down into two parts: selecting and arranging the letters, and selecting and arranging the digits.

### Step 1: Calculate the number of ways to choose and arrange the letters
1. **Choose 2 different letters from the 26 letters of the alphabet.**
- The number of ways to choose 2 letters from 26 is given by permutations since the order matters. This is calculated using the formula for permutations:
\[ P(n, r) = \frac{n!}{(n-r)!} \]
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