The Permutations of N items is N!

#### What is a permutation in Math?

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

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*.

As the tree diagram below illustrates, there are a total of 6 ways to arrange the letters *A*,
*B* and *C*.

All possible arrangements of the three letters are :1) ABC 2) ACB 3) BCA 4) BAC 5) CAB 6) CBA

#### What about 4 letters?

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.