Question-56

• How many seven digit phone numbers are possible, assuming that the first digit can’t be a \(\displaystyle 0\) or a \(\displaystyle 1\)?
• How would this answer change if no phone number can start with \(\displaystyle 911\)?

Answer

• \(8 \times 10^{6}\)
• \(8 \times 10^{6} - 10^{4}\)

Solution

The first slot has \(\displaystyle 8\) possibilities. The remaining slots have \(\displaystyle 10\) possibilities. Therefore, the number of phone numbers is \(\displaystyle 8\times 10^{6}\). For the second part, we subtract all phone numbers starting with \(\displaystyle 911\). There are \(\displaystyle 10^{4}\) such numbers. So the required answer is \(\displaystyle 8\times 10^{6} -10^{4}\).