Both count ways to select items from a group, but they differ on whether order matters.
Formula: C(n, r) = n! ÷ [r! × (n−r)!]
Example: Choosing 3 toppings from 5 available. Choosing pepperoni, mushrooms, onions is the same as onions, mushrooms, pepperoni — it's one combination.
Formula: P(n, r) = n! ÷ (n−r)!
Example: A race with 8 runners, top 3 get medals. 1st, 2nd, and 3rd are different placements, so order matters.
From 5 people, choose 3 for a team: C(5,3) = 5! ÷ (3! × 2!) = 120 ÷ 12 = 10 combinations. If assigning 3 distinct roles: P(5,3) = 5! ÷ 2! = 120 ÷ 2 = 60 permutations.