Calculate Permutations and Combinations
Calculate nPr (permutations) and nCr (combinations). How many ways to arrange or choose from a group.
Permutations vs Combinations
Permutations (nPr): Order matters. How many ways to arrange r items from n? Formula: n!/(n-r)!. Picking 1st, 2nd, 3rd place from 10 runners: 10P3 = 720 arrangements. Combinations (nCr): Order doesn't matter. How many ways to choose r items from n? Formula: n!/(r!(n-r)!). Choosing a 3-person committee from 10 people: 10C3 = 120 groups.
When to Use Each
Permutations: Passwords, rankings, race results, phone numbers — anywhere the order changes the outcome. Combinations: Lottery picks, team selections, pizza toppings, card hands — anywhere a set is a set regardless of order. Ask yourself: "Does rearranging the selection create a different outcome?" Yes → permutation. No → combination.
The lottery is the most visible application of combinations. Powerball odds (1 in 292 million) mean: if you bought 100 tickets per week, you would expect to win once every 56,000 years. The expected value of a $2 Powerball ticket is about $0.85 — a 57% loss on every dollar played.
