Why Order Matters

Consider a podium with gold, silver, and bronze medals. Giving gold to Alice and silver to Bob is different from the reverse. From 10 athletes, the number of possible podiums is 10 times 9 times 8 equals 720 — far more than the 120 combinations of choosing any 3.

Ranking the top 3 finishers from 20 competitors: P(20,3) = 20 × 19 × 18 = 6,840 outcomes. Notice how much larger this is than C(20,3) = 1,140. Permutations always outnumber combinations because every combination spawns multiple orderings.