Solve the problem - How many three digit numbers do not contain a five? Show evidence of solving the problem in a systematic way.
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To solve this problem systematically, we can analyze each digit of the three-digit number separately.
First, let's consider the hundreds digit. Since it cannot be a five, it can be any digit from 1 to 9 (excluding 5). Therefore, there are 9 options.
Next, let's move on to the tens digit. Similar to the hundreds digit, it cannot be a five. Hence, there are 9 options available as well.
Finally, let's consider the units digit. Again, it cannot be a five, so there are 9 options available.
To find the total number of three-digit numbers satisfying the given condition, we need to multiply the choices for each digit together since each digit choice is independent of the others.
9 choices for the hundreds digit × 9 choices for the tens digit × 9 choices for the units digit = 729.
Therefore, there are 729 three-digit numbers that do not contain a five.
Alternatively, you can verify this result by manually listing all the three-digit numbers without a five, starting from 100 and ending with 999. However, this approach would be time-consuming and less efficient compared to the systematic method explained above.