In a set of three-digit numbers, the last digit determines whether the number is odd or even. For a number to be odd, its last digit must be one of the odd digits: 1, 3, 5, 7, or 9.
Therefore, there are 5 choices for the last digit. For the hundreds and tens digits, each can take any value from 0 to 9, giving 10 choices for each.
So, the total number of three-digit odd numbers is given by multiplying the number of choices for each digit:
\[ 5 \ (choices \ for \ the \ last \ digit) \times 10 \ (choices \ for \ the \ hundreds \ digit) \times 10 \ (choices \ for \ the \ tens \ digit) = 500 \]
Therefore, there are 500 three-digit odd numbers.
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