possible phone numbers. A telephone number consists of seven digits with restric

Question

possible phone numbers. A telephone number consists of seven digits with restriction that the first digit cannot be 1 or 0.

a- How many distinct numbers are possible?

b-How many distinct telephone numbers are possible with three digit are codes preceeding the seven digit number, where the first digit of the area code cannot be 0 or 1.

c- with the increasing use of cell phones and paging systems, our society is beginning to run out of usable phone numbers. Various phone companies are developing phone numbers that use 8 digits instead of 7. How many distinct phone numbers can be made using a three digit area code followed by eight digit phone number, where the first digit of the area code cannot be 0 or 1?

Explanation / Answer

a) Since we have 10 choices for all digits from 2 to 7 and 8 choices for the first digit:

Total distinct numbers possible = 8*10*10*10*10*10*10 = 8000000

b) For three digits code, we have 8 possibilities for first code digit and for remaining 2 digits, we have 10 possibilities. So,

Total distinct numbers possible = 8*10*10*8000000 = 6400000000

c) For 8 digit numbers with 3 digit area code, we will have 8 possibilities for two digits i.e. first digit of area code and first digit of number, for rest of the 9 digits, we have 10 options available i.e. 0 to 9. Hence,

Total distinct numbers possible = 8*10*10*8*10*10*10*10*10*10*10 = 64000000000

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