nPr counts the ordered arrangements of r items chosen from n:
nPr = n! / (n − r)! = n × (n−1) × … × (n − r + 1)
Use the product form, not two factorials. It multiplies only r numbers and never builds the enormous n!.
Read it as: n choices for the first slot, n−1 for the second, … Counting slot by slot like this is the key to most permutation problems.