A student ID number is a letter of the alphabet followed by 2 digits. How many different IDs are possible if the digits can be repeated?

First, there are 26 distinct alphabets and 10 distinct digit numbers.

Then, the first digit of ID has 26 possibilities.

For the rest of 2 digits, the total cases are 10*10 = 100 possibilities.

However, there are 10 cases are repeated when two digits are the same. so you have to subtract it by 10

So answer will be 26 * (100-10) = 23400