In the permutation formula P(n, r), why is n factorial divided by (n - r) factorial?

1. The quantity n! counts the orderings of all n objects at once. 2. Only r of them are actually being placed in order, so the remaining n - r are irrelevant. 3. Dividing by (n - r)! cancels the orderings of those unwanted items. 4. Dividing instead by r! would remove the orderings of the chosen items, and that is what turns a permutation count into a combination count. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.5 Counting Principles_