SOLUTION: This is not from a text book but a question my instructor posed to me. I am not sure how to figure it out. Can someone please help me with it? Suppose we have a list of zip co

Question 195613: This is not from a text book but a question my instructor posed to me. I am not sure how to figure it out. Can someone please help me with it?
Suppose we have a list of zip codes that is only the 5-digit without the extension and there is no replacement or repetition. How many possible zip codes do we have?

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Note: I'm assuming that zero can be used as the first digit.

Method # 1:

Number of Possible Permutations = Number of Choices 1st Digit * Number of Choices 2nd Digit * Number of Choices 3rd Digit * Number of Choices 4th Digit * Number of Choices 5th Digit

Number of Possible Permutations = 10 * 9 * 8 * 7 * 6

Number of Possible Permutations = 30,240

So there are 30,240 different zip codes

------------------------------------------------------------

Method # 2

Since there are 10 possible numbers to choose from and there are 5 positions to place them in, this means that and

Since order does matter, we must use the permutation formula:

Start with the given formula

Plug in and

Subtract to get 5

Expand 10!

Expand 5!

Cancel

Simplify

Now multiply 10*9*8*7*6 to get 30,240

So 10 choose 5 (where order does matter) yields 30,240 unique permutations

So once again, there are 30,240 different zip codes.

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