Combinations and Permutations Calculator

Use this calculator when you pick r items from a set of n. Combinations C(n, r) ignore order (hands of cards, committees). Permutations P(n, r) count order (race places, PIN codes from distinct digits). You need 0 ≤ r ≤ n; n and r are truncated to integers.

The formulas are: C(n, r) = n! / (r! (n − r)!) and P(n, r) = n! / (n − r)!. The binomial coefficient is C(n, r). Row n of Pascal’s triangle is C(n, 0) … C(n, n); this page returns one pair, not the whole row.

n: Size of the set.

r: How many you pick. Need r ≤ n.

C(n, r): Combinations (order does not matter).

P(n, r): Permutations (order matters).