Question

New York is adding new numbers to it's current 718 area code. The format is (718) XXX-XXXX)where all the x's are numbers. If the following restrictions are applied; the 1st and last numberscan not be 0 or 8 and the 3rd number in the series can only be 0-6. How many phone numbersare possible? (remember without restrictions, each number has 10 available digits)

Answer 1

Answer:

4,480,000 phone numbers are possible

Explanations:

Without restrictions each digit has 10 availble numbers (0 - 9)

Let us cosider the possibilities for each digit

For the first digit:

Since it cannot be 0 or 8, it means it can contain only digits 1, 2, 3, 4,5,6,7,9(i.e. 8 digits)

The first digit can only include 8 numbers

For the second digit:

It has no restriction, so it can contain digits 0 - 9 (10 numbers)

The second digit can contain 10 numbers

For the third digit:

It can only contain digits from 0 to 6 (7 numbers)

The third digit can contain 7 numbers

For the fourth, fifth and sixth digits:

They do not have restrictions, so they can contain 10 numbers each

For the last (7th) digit:

Since it cannot be 0 or 8, it means it can contain only digits 1, 2, 3, 4,5,6,7,9(i.e. 8 digits)

The last digit can only include 8 numbers

Therefore the number of possible phone numbers = 8 *10*7*10*10*10*8

The number of possible phone numbers = 4,480,000