Combinations & Permutations

A coach must pick 5 starters from 8 players. How many different lineups are possible? You could try to list them — but the list runs into the thousands. And here's the twist: if the coach assigns POSITIONS too (point guard, center, ...), the count balloons to tens of thousands. Same 8 people, same 5 chosen — wildly different totals. The difference is whether ORDER matters. Two simple formulas, one division apart, count both cases instantly. This is the counting engine underneath every probability you'll ever compute.