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

Algebra ->  Permutations -> 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      Log On


   

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) About Me  (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


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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 n=10 and r=5



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




n%21%2F%28n-r%29%21 Start with the given formula



10%21%2F%2810-5%29%21 Plug in n=10 and r=5



10%21%2F5%21 Subtract 10-5 to get 5



Expand 10!
%2810%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F5%21



Expand 5!
%2810%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F%285%2A4%2A3%2A2%2A1%29



%2810%2A9%2A8%2A7%2A6%2Across%285%2A4%2A3%2A2%2A1%29%29%2F%28cross%285%2A4%2A3%2A2%2A1%29%29 Cancel



10%2A9%2A8%2A7%2A6 Simplify




30240 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.