Question

The author spoke with a representative of the U.S. Postal Service and obtained the following information about zip codes. A five-digit zip code consists of five digits, of which the first three give the sectional center and the last two the post office or delivery area. In addition to the five-digit zip code, there is a trailing plus four zip code. The first two digits of the plus four zip code give the sector or several blocks and the last two the segment or side of the street. For the five-digit zip code, the first four digits can be any of the digits $0-9$ and the fifth any of the digits $1-8 .$ For the plus four zip code, the first three digits can be any of the digits $0-9$ and the fourth any of the digits 1-9. a. How many possible five-digit zip codes are there? b. How many possible plus four zip codes are there? c. How many possibilities are there in all, including both the five-digit zip code and the plus four zip code?

          The author spoke with a representative of the U.S. Postal Service and obtained the following information about zip codes. A five-digit zip code consists of five digits, of which the first three give the sectional center and the last two the post office or delivery area. In addition to the five-digit zip code, there is a trailing plus four zip code. The first two digits of the plus four zip code give the sector or several blocks and the last two the segment or side of the street. For the five-digit zip code, the first four digits can be any of the digits $0-9$ and the fifth any of the digits $1-8 .$ For the plus four zip code, the first three digits can be any of the digits $0-9$ and the fourth any of the digits 1-9.
a. How many possible five-digit zip codes are there?
b. How many possible plus four zip codes are there?
c. How many possibilities are there in all, including both the five-digit zip code and the plus four zip code?

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Added by Brett A.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Jason Horton

02/25/2023

Step 1

For the five-digit zip code, the first four digits can be any of the digits $0-9$, and the fifth digit can be any of the digits $1-8$. So there are $10$ choices for each of the first four digits and $8$ choices for the fifth digit. Show more…

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The author spoke with a representative of the U.S. Postal Service and obtained the following information about zip codes. A five-digit zip code consists of five digits, of which the first three give the sectional center and the last two the post office or delivery area. In addition to the five-digit zip code, there is a trailing plus four zip code. The first two digits of the plus four zip code give the sector or several blocks and the last two the segment or side of the street. For the five-digit zip code, the first four digits can be any of the digits $0-9$ and the fifth any of the digits $1-8 .$ For the plus four zip code, the first three digits can be any of the digits $0-9$ and the fourth any of the digits 1-9. a. How many possible five-digit zip codes are there? b. How many possible plus four zip codes are there? c. How many possibilities are there in all, including both the five-digit zip code and the plus four zip code?

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Transcript

00:01 All right, in your question, you're asked to determine how many possible zip codes there are.

00:05 That's the five -digit version.

00:07 How many possible plus four zip codes, the four numbers at the end? and then how many total possibilities if we include all nine numbers? so for the first five -digit zip code, i have five digits to choose from here.

00:23 The first four digits, it says, can be anything from zero to nine.

00:32 But the last digit can only be from 1 to 8.

00:37 Okay, there are 10 numbers from 0 to 9, so that means we could choose any of the 10 for those numbers.

00:45 There would only be 8 numbers from 1 to 8.

00:48 Now to get the total possible outcomes, we simply multiply those values.

00:55 So 10, i can just do 10 to the 4th power times 8, and that works out to be 80 ,000 zip codes.

01:08 Now the plus 4 zip code has restrictions on the numbers.

01:13 It says the first three digits can be anything 0 to 9, which would be 10, 10, 10.

01:22 The last one can be 1 to 9, and that would be 9 numbers.

01:27 Again, we just multiply those out.

01:31 So i'm doing 10 to the third power times 9.

01:36 And we end up with 9 ,000.

01:40 Now, for the total possibilities, basically we just put this whole group together with this whole group and we just keep multiplying.

01:50 Or i could take the results and multiply them, which is the quicker way to do it...

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