GED Mathematical Reasoning: Permutations

  • A permutation is used to find the number of ways to accomplish something when the order DOES matter.
  • This is a bit different than our discussion of combinations, where the ordering does NOT matter.


Example 1

Sebastian has 3 projects to complete at work today and he must decide in what order to complete them. How many possible orderings of three tasks are available to Sebastian?


In example one, we must help Sebastian sequence the three projects on his “to do” list, however it’s important to note that a listing of: project 1, project 2, and project 3 is a completely different outcome than a listing of: project 3, project 2, and project 1.

To determine the number of possible orderings of three projects available to Sebastian, we know that there are three projects that can fill the first slot on his “to do” list. That leaves two projects that can fill the second slot on his list and one project that can fill the third slot.


From here, we can find the number of possible orderings of three projects by multiplying: three times two times one. So the number of possible orderings, or permutations, of the three projects is equal to 6.

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Example 2

Tara needs to choose an access code for her home security system that consists of four different digits using the digits 0 through 9. How many codes can be formed in this way?


First note that in example two, order matters. An access code of 3258 is very different from an access code of 8523.

There are ten digits to choose from: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. And all four digits in the code must be different.

There are 10 ways to choose the first digit in the access code. After that first digit is selected, it cannot be used again. That leaves 9 digits from which to select the second digit in the code. After the second digit is selected, it cannot be used again meaning that there are 8 options for the third digit. This leaves 7 digits for the fourth digit.


Since we only need four digits in the access code, we will stop there. Since the word “The number of possible access codes that can be created using the given parameters can be found by multiplying 10 times 9 times 8 times 7.

So there are 5040 possible access codes.

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