Question

Within a given area code, calculate the total number of seven-digit numbers are available, given the restrictions that the first three digits cannot be $911$ or $411$ and the first digit cannot be a $1$ or a $0$.

• A. $604,800$
• B. $2,893,401$
• C. $6,380,000$
• D. $7,980,000$
• E. $8,000,000$

Answer 1

Answer: (D)

$7,980,000$

First digit cannot be $1$ or $0$ and each digit in seven digit number can be any digit in between $0$ and $9$ inclusive.
Number of possible seven digit numbers are $8\times 10\times 10\times 10\times 10\times 10\times 10=8000000$.
But the number should not start with $911$ and $411$.
So the numbers starting with those are $2\times 10\times 10\times 10\times 10=20000$.
So, the resultant answer is $8000000-20000=7980000$