Answer:
1) 6.4 × 10^5 combinations
2) 40,000,000phone numbers
3) 633%
Step-by-step explanation:
1) U.S. phone numbers:
area code = 3-digit, exchange code= 3-digit, subscriber code at the end= 4digit
and exchange code cannot be 0 or 1
Since number system is from 0-9:
For 3 digit area code:
The first digit of area code cannot be 0 or 1, the numbers would be between 2-9. When you count 2-9 =8 numbers
The 2 and 3 digit would be between 0-9. When you count 0-9 = 10 numbers for both
Combinations of area code = 8 × 10 × 10 = 800 different combinations.
For exchange code:
The first digit of exchange code cannot be 0 or 1, the numbers would be between 2-9. When you count 2-9 = 8 numbers
The 2 and 3 digit would be between 0-9. When you count 0-9 = 10 numbers for both
Combinations of exchange code = 8 × 10 × 10 = 800 different combinations.
The number of different combinations of area code and exchange code that is possible = 800 × 800
= 640,000 = 6.4 × 10^5 combinations.
2) Area code (3digit): 1st digit falls between 2-9 = 8numbers, 2 others are 10 numbers each.
Exchange code (3 digit): 1st digit falls between 2-9 = 8numbers, 2 others are 10 numbers each.
Subscriber number (4 digit) falls between 0-9 = 10 numbers each
For each of the five area codes combination(exchange code, subscriber number),
we have 8 × 10 × 10 = 800 possible exchange codes
10 × 10 × 10 × 10 = 10,000 possible subscriber numbers.
The total number of unique phone numbers possible (in compliance with NANPA standards) using the 301, 410, 240, 443 and 667 area codes:
= 5 × 800 × 10,000 = 40,000,000 phone numbers.
3) There are 8,000,000 unique phone numbers for the 301 area code.
If these numbers were exhausted in 44 years, then number of phone numbers assigned yearly:
= 8,000,000 ÷ 44 = 181,818.18
There are 8,000,000 unique phone numbers for the 410 area code.
If these numbers were exhausted in 6 years, then number of phone numbers assigned yearly:
= 8,000,000 ÷ 6 = 1,333,333.33
For the 410 area code, difference in numbers assigned yearly:
= 1,333,333.33 - 181,818.18 = 1,151,515.15
phone numbers assigned per year. Percentage increase = (increase/number of 301code assigned yearly)×100
(1,151,515.15 ÷ 181,818.18) ×100 = 633.33 ≈ 633%
The percent increase from the rate at which 301 area code phone numbers were assigned to the rate at which numbers with a 410 area code were assigned = 633%
