Final answer:
Using the counting principle, the number of different three-letter initials from the English alphabet with no letters repeated is the product of the number of possibilities for each position: 26 x 25 x 24, yielding 15,600 different combinations.
Step-by-step explanation:
To calculate how many different three-letter initials there are with no letters repeated, we use the basic counting principle. Assuming the initials are taken from the English alphabet, which contains 26 letters, for the first initial there are 26 possible letters. For the second initial, since one letter has already been used, there are only 25 letters left to choose from. Finally, for the third initial, there are 24 letters remaining because two letters have been used up.
The total number of different three-letter initials with no repeated letters is the product of these possibilities, so we calculate 26 × 25 × 24. Doing the math gives us 15,600 different three-letter initials. This is how we apply the counting principle to determine the number of combinations without repetition.