Question

In a small town in South Georgia, how many phone numbers are possible with the following restrictions?

*The first digit of the phone number cannot be numbers 0-6.

*The second number cannot be numbers 0-2.

*The third number cannot be a zero.

*There will be no restrictions for all other numbers

*There will be a total of 3 area codes

Answer 1

Answer: 5,670,000 phone numbers

Explanation:

Without restrictions, a single digit can be one of 10 choices, numerals 0 through 9

area code has 3 choices (seems silly for a 'small town', but that is what the problem says, right?)

1st digit after area code has 3 choices - 7, 8, or 9

2nd digit after area code has 7 choices - 3, 4, 5, 6, 7, 8, 9

3rd digit after area code has 9 choices - 1, 2, 3, 4, 5, 6, 7, 8, 9

4th digit after area code has 10 choices - 0 through 9

5th digit after area code has 10 choices - 0 through 9

6th digit after area code has 10 choices - 0 through 9

7th digit after area code has 10 choices - 0 through 9

We multiply the possible choices for each digit to get the overall number of choices ---> 3*3*7*9*10*10*10*10 = 9*63*10,000 = 5,670,000

Answer ---> 5,670,000 possible phone numbers