Final answer:
To find the number of numbers less than 1000 with distinct digits, consider each digit separately and multiply the number of possibilities for each digit together. The correct answer is 720.
Step-by-step explanation:
To find the number of numbers less than 1000 with distinct digits, we can consider the first digit. Since it can't be zero, there are 9 possibilities for the first digit. For the second digit, we can choose any digit except for the one already chosen for the first digit, so there are 9 possibilities. Similarly, for the third digit, we can choose any digit except for the ones already chosen for the first and second digits, so there are again 9 possibilities. Therefore, the total number of numbers with distinct digits is 9 x 9 x 9 = 729. However, we have to exclude the number zero, so the final answer is 729 - 1 = 728.
Therefore, the correct answer is 720 (option D).