Permutation calculator
A permutation counts ordered arrangements: P(10,3) = 720 ways to award gold, silver and bronze among ten runners. Allowing repetition gives 10³ = 1,000 instead, which is the right count for a three-digit code.
How to count permutations
The repetition distinction is what separates a podium from a padlock. Three medals among ten runners is 720. Nobody wins twice. A three-wheel padlock with ten digits is 1,000, because each wheel is independent. The padlock is larger despite the same n and r, which is why combination locks are named misleadingly: they are permutation locks, and order very much matters.
Questions
n! divided by (n−r)! — the number of ordered arrangements of r items from n.
720, since order matters and nobody wins twice.
It becomes n to the power r. Ten digits over three wheels gives 1,000.
No — order matters, so it is a permutation lock. The name is a long-standing misnomer.
nPr equals nCr times r!, because each combination can be ordered r! ways.