Calculate the number of ways to arrange or choose items.
Permutations (nPr) count the number of ways to arrange r items from n distinct items where order matters. Combinations (nCr) count subsets where order does not matter. For example, picking a president, VP, and treasurer from a group is a permutation; picking a committee of 3 is a combination.
P(n,r) = n! / (n−r)!. C(n,r) = n! / (r! × (n−r)!). For n=8, r=3: P = 8×7×6 = 336, C = 336 / 3! = 56.
Use permutations when the order or arrangement matters (e.g., race positions, passwords, seating arrangements). Use combinations when the selection is unordered (e.g., lottery numbers, committee members, hand of cards). A helpful test: if swapping two chosen items gives a different result, use permutations.
If r exceeds n, both P(n,r) and C(n,r) are zero because you cannot choose or arrange more items than are available. The calculator enforces r ≤ n for valid results.