Answer
People can have 15600 different 3 letter initials without repeating the same letter.
Work Step by Step
We assume only capital alphabets (A - Z)
The first letter has 26 choices
The second letter has 25 choices (we cannot choose the first letter again).
The third letter has 24 choices (we cannot choose first or second letter again).
So, total ways = 26 x 25 x 24 = 15600