Area codes are made up of three - digit numbers

a. if all numbers can be used for each digit, how many area codes are possible?

b. how many area codes would be possible if repetition is not allowed?

There are 10 numbers from 0 to 9 which may be used for the 3-digit code. To answer the questions above, make use of the Fundamental Principles of Counting.

a. There are 10 digits that may be used in all of the 3 places of the code:

10 x 10 x 10 = 1000

b. Since repetition is not allowed. On the first place of the code, 10 digits are allowed. After using any of the digits, only 9 are available for the second digit and 8 on the third.

10 x 9 x 8 = 720

Thus, there are 1000 and 720 possible 3-digit codes in cases a and b, respectively.