How many 3-digit odd numbers exist, with no repetition? Ex: 871 counts, but 777 does not.

Sure, let's break it down:

1. A 3-digit number has three places: hundreds, tens, and units.

2. Since the number is odd, the unit place can be filled by any of the 5 odd numbers from 0 to 9, which are 1, 3, 5, 7, and 9.

3. The hundreds place can't be 0 (because then it wouldn't be a 3-digit number) and it can't be the same as the units digit. So it can be filled by any of the remaining 8 digits.

4. The tens place can't be the same as the hundreds or units digit, so it can be filled by any of the remaining 7 digits.

5. Therefore, the total number of 3-digit odd numbers with no repetition is 5 (choices for the units place) * 8 (choices for the hundreds place) * 7 (choices for the tens place) = 280.