The possible combinations of 1 digit code is 10.

They are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

(a)

There are 10 possibilities for each digit.

ZIP codes are possible if the numbers 0 through 9 are used for each of the five digits .

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(b)

First digit is should be 0 only.

Possible combinations for second, third, fourth digits are 1, 2, 3, 4, 5, 6, 7, 8, 9.

Possible combinations for fifth digit is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

There is only one possibility for the first digit, 10 possibilities for the fifth digit, and 9 possibilities for the other digits.

So the total number of possibilities

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(c)

Postal Service introduced the ZIP+4.

There are 10 possibilities for each digit.

ZIP+4 codes are possible if the numbers 0 through 9 are used for each of the five digits .

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Additional ZIP codes = number of ZIP+4 codes - number of  five digit ZIP codes.

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(a) .

(b) .

(c) .