Answer: 531441
The Multiplication Principle of Counting is a way of figuring out the number of outcomes in a given problem. Basically, we need to multiply the events together to get the total number of outcomes.
For this problem, we have the numbers 0-9 except 4. That would be a total of 9 possible numbers each place in the 6-digit phone number.
Since any digit on the number can be any number, this would mean that each digit in the phone number would have 9 possible numbers as well.
Therefore, the total number of 6-digit numbers would then be:
[tex]9\times9\times9\times9\times9\times9=531441[/tex]
There would be a total of 531441 6-digit phone number that does not contain the number 4.
