Simplistically, a permutation is just the number of ways that we can arrange any number of objects in a set of things.
Here's an example:
Suppose I have three objects A, B and C, and I want to arrange them in all possible ways.
Well, we could have
A B C
A C B
B A C
B C A
C A B
C B A
Note that this is just 6 ways.
In mathematics, we often express the number of possible arrangements of N objects as N! .... the "!" is known as a "factorial."
In the above example, we have 3! ways of arrangement = 3*2*1 = 6.
Then, the number of ways to arrange 4 objects in a set is just 4! = 4*3*2*1 = .24.
And the number of ways to arrange 5 objects in a set is just 5! = 5*4*3*2*1 = .120.
Etc.
I hope this helps.
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