Final answer:
To calculate the number of different three-digit numbers that can be created in a pick 3 lottery with six balls, we multiply the number of options for each digit, resulting in 120 different numbers.
Step-by-step explanation:
When determining how many different three-digit numbers can be created from a selection of six numbered balls in a pick 3 lottery, we are dealing with a permutation problem since the order in which we pick the balls matters. Since there is no replacement, we have six options for the first digit, five options for the second (after one has been selected), and four options for the third. Therefore, the total number of different three-digit numbers that can be created is calculated by multiplying the number of options for each position.
The calculation would be: 6 (for the first digit) × 5 (for the second digit) × 4 (for the third digit) = 120 different three-digit numbers.