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

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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


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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.