There are 160 possibilities for area codes
We are required to find all the combinations for different area codes
It is given to us that the conditions for the tree digit area code are:
first digit could be any number from 4 through 8,
the second digit was either 4 5 6 or 7, and the third digit could be any number except 2 or 7
Using the conditions above, the digits which can be first digit of code = 4 through 8 =4,5,6,7,8
the digits which can be second digit of code= 4,5,6,7
the digits which can be third digit of code = 0,1,3,4,5,6,8,9
number of possibilities for first digit= 5
number of possibilities for second digit=4
number of possibilities for third digit= 8
Therefore, total number of possibilities of code = number of possibilities of first digit x number of possibilities of second digit x number of possibilities of third digit = 5 x 4 x 8=160
Therefore, there are 160 possibilities for area codes
For further reference:
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