Well, well, well, I am realizing that teaching is not all it's cracked up to be. :)
Permutations are sometimes defined as any possible arrangement, or ordering, of the distinct items in a set. Or a way to arrange things in which order is important.
An example question:
If a softball league has 10 teams, how many different end of season rankings are possible? (Assume no ties)
Since we are ranking these teams that means the order is important. So we can use permutations to help us out.
We already know the formula is nPr from previous posts. So n is the number of teams we have to choose from. And we know from the information in the question that there are 10 teams.
R is the number of teams we are ranking at a time.
Again we know that r=10.
You put the numbers into the formula and you wind up with 10P10. After that you have to do the multiplication which is 10*9*8*7*6*5*4*3*2*1=3628800.
So this tells us that there are 3,628,800 ways to rank those 10 teams.
I hope my example question helped!