Answer: 720
Work Shown
P(n,r) = (n!)/( (n-r)! )
P(6,6) = (6!)/( (6-6)! )
P(6,6) = (6!)/( 0! )
P(6,6) = (6*5*4*3*2*1)/( 1 )
P(6,6) = 6*5*4*3*2*1
P(6,6) = 720
The exclamation marks indicate factorial.
A real world application could be this: you have 6 books you want to arrange on a shelf. There would be 720 ways to do this using the permutation formula shown above. Notice how P(n,n) = n! or P(n,r) = n! only if n = r.
It might seem confusing that 0! = 1, but I tend to think of it like saying "there's 1 way to arrange nothing". There might be a better explanation for this, so feel free to search one out.
