Assume the following rules are true for any telephone number in North America:
- A telephone number in North America consists of ten numbers
- a three-digit area code,
- followed by a three-digit exchange/prefix,
- followed by a four-digit line/subscriber number
….so the format is (AAA-EEE-XXXX).
- The area code cannot start with a 0 or 1.
- The exchange cannot start with a 0 or 1.
- Other than the rules in II. and III. above, any digit 0-9 can be used in any of the ten places in a phone number.
How many different seven-digit phone numbers (excluding the area code, including only the exchange and line/subscriber number) can be formed?
I would start off by drawing lines…
7 (because says excluding area code), 8 (because said exchange can’t start with 0,1 so I have 8 other options), 10 (because of the last thing it says is “any digit 0-9 can be used in any ten places in a phone number)
So I would multiply them now… 7*8 = 56, 56 *10 = 560
Where did I go wrong?