Final answer:
There are 15,600 different three-letter initials that can be created when no letters are repeated, calculated by multiplying 26 options for the first letter by 25 remaining options for the second, and 24 for the third (26 x 25 x 24).
Step-by-step explanation:
To determine how many different three-letter initials can be formed with no letters repeated, we use counting principles from combinatorics. Specifically, we look at permutations since the order of initials matters. We have 26 options for the first letter, 25 for the second (since one letter has already been used), and 24 options for the third letter.
The total number of different three-letter initials is calculated by multiplying these numbers:
- 26 options for the first letter (A to Z)
- 25 remaining options for the second letter
- 24 remaining options for the third letter
The calculation will be:
26 × 25 × 24 = 15,600
Therefore, there are 15,600 different three-letter initials one can create with no letters repeated.