Final answer:
To determine the total number of distinct three-digit numerals formed from the digits 1, 5, and 8 with no repetition, you multiply the number of choices for each digit's position, resulting in 3 × 2 × 1 = 6 different numerals.
Step-by-step explanation:
To answer the question of how many different three-digit numbers can be formed from the digits 1, 5, and 8 without repetition, we should consider the number of choices we have for each digit's place in the numeral. For the first digit, we have 3 choices (1, 5, or 8). Once the first digit is chosen, we have 2 remaining choices for the second digit. Finally, we have only 1 choice left for the third digit, since the remaining digit cannot be repeated.
So, the total number of different three-digit numerals that can be formed is calculated by multiplying the number of choices for each digit place:
3 (for the first digit) × 2 (for the second digit) × 1 (for the third digit) = 6 different numerals.