P(6,2) = 6!/(6-2)! = 6!/4! = (6 × 5 × 4!)/(4!) = 6 × 5 = 30.
P(10,3) = 10!/7! = 10 × 9 × 8 = 720.
Notice you don't compute full factorials. Cancel common terms and multiply the top r factors.
P(4,4) = 4!/0! = 4! = 24. This is the full arrangement case.