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Just Show me the formula:

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The Permutations of N items is N!

What is a permutation in Math?

question
A Permutation is an ordered group of items.


How many permutations are there for 2 letters ?

In other words, how many different ways can you arrange the two letters like AB? Remember: order matters
question
As an example, consider the permutations of the letters A and B. Just think about how many different ways you can arrange A and B. The key to a permutation is that order matters!!!!
  • AB
  • BA
As you can see, the only difference between our two permutations is the order. In our first one "AB," A is first and B is last. In the second one, "BA," all that we did was switch the order so that B goes first and A last.

What about 3 letters?

If we add the letter C to our items. We now have a permutation of 3 items: the letters A, B and C.
question
As the tree diagram below illustrates, there are a total of 6 ways to arrange the letters A, B and C.
Diagram of Multplication Counting Principle
All possible arrangements of the three letters are :1) ABC 2) ACB 3) BCA 4) BAC  5) CAB  6) CBA


What about 4 letters?

question
We are going to order the letters A, B, C and D.
If we go by the formula, the total number of ways to organize four items, which in this case are the letters A, B, C and D, should be equal to 4!. 4! = 4 ×3×2×1 = 24


Locker Permutation Generator

Applied Example: A school bought a special kind of lock for all student lockers. Every student had to create his or her own pass code made up of 4 different numbers from 0-9.

This is an example of a common kind of problem involving ordering numbers. Notice how the order matters. If you  made up a pass code of "3-5-9-0" but tried to use the same numbers in a different order like "5-3-9-0" you would not be able to get into your locker! Try the pass code generator below to see that no matter what numbers are used for the first, second, third and fourth digits, there are always the same number of available numbers for the following digit.

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Next: Permutations
with repeated items