A zip-code is a five-digit number identifying where in the U.S. an address is located. The first four digits in a zip code can be any number 0-9, but the fifth digit cannot be 0. In addition to this, each address has a “plus-four” code that more specifically identifies the location of an address within a town or city. Similar to the main five-digit zip-code, the first
three digits in the “plus
-four” code can be 0-9, but the fourth digit cannot be 0.
a.)How many five-digit zip codes are possible in the U.S.?
9 * 10^4
To determine the number of possible five-digit zip codes in the U.S., we need to consider the range of values each digit can take.
The first digit in a zip code can be any number from 0 to 9, so there are 10 possible options (0, 1, 2, 3, 4, 5, 6, 7, 8, 9).
The second digit also has the same range of 0 to 9, so again there are 10 possible options.
The third digit, fourth digit, and fifth digit can also be any number from 0 to 9, resulting in 10 possible options for each of them.
So, the total number of possible five-digit zip codes is calculated by multiplying the number of options for each digit:
10 options for the first digit * 10 options for the second digit * 10 options for the third digit * 10 options for the fourth digit * 10 options for the fifth digit = 10 * 10 * 10 * 10 * 10 = 100,000.
Therefore, there are 100,000 possible five-digit zip codes in the U.S.