Permutation

Permutations are arrangements of items in a particular order, e.g., of any three items ABC, AB is a different arrangement than BA.

This is how permutations are denoted: n Pr, where it is a Permutation of n items arranged by r items at a time. Therefore, r ≤ n.

If r = n in nPr, then nPr = n!.

Here's how nPr is formulated:

$$nPr = \frac{n!}{(n-r)!}\,$$

How It Works
Here's a demonstration of how nPr works.

Suppose we have the letters ABCDE. How many possible arrangements can I have if I do so three at a time?

Rather than spending time actually arranging and counting said arrangements, let's figure it out with some math.

Let's start crunching in some numbers.

Since n = 5, and r = 3, nPr becomes 5P3.

Since we don't want to bother with the complicated formula, let's just take this shortcut:

To get what we must multiply, we take n and multiply it by (n–1), then that by (n–2), and so on until we have r terms.

E.g., if we were to find 4P2, then 4P2 = 4 * 3 = 12.

Therefore, 5P3 = 5 * 4 * 3 = 60.

There are 60 possible permutations of ABCDE.