The North American numbering plan (NANP) specifies the format oftelephone numbers in the U.S., Canada, and many parts of NorthAmerica. A number in this plan consists of ten digits whichare split into a three-digit area code, a three-digit office code,and a four-digit station code. Because of signalingconsiderations, there are certain restrictions on some of thesedigits. To specify the allowable format, let X denote a digitthat can take any of the values 0 through 9, let N denote digitthat can take any of the values 2 through 9, and let Y denote adigit that must be a 2 or 1.

(A) In the 1960s, telephone numbers had the formNYX-NNX-XXXX. How many phone numbers were possible under thissystem?

(B) A new plan is currently in place. Telephone numbershave the form
NXX-NXX-XXXX. There are some additional restrictions. Numbersof the form
212-718-XXXX are not used because 212 and 718 are both area codesin New York City and numbers of this form would causeconfusion. Area codes of the form N11 are not used. Area codes of the form N9X are reserved for future expansion andnot currently in use. Area codes of the form 37X and 96X arealso reserved for future use. How many phone numbers arepossible under this system?

(C) Continue with the plan described in part b with a couplemore restrictions. Assume that Jenny (8675309 video) causedenough problems with prank calls that numbers of the formNXX-867-5309 are no longer used. Additionally, assume thatnumbers of the form NXX-555-0100 through NXX-555-0199 are reservedfor fictional use. How many telephone numbers are possibleusing this system?

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