Instantly calculate the number of combinations C(n,r) and permutations P(n,r) — useful for lottery, probability and statistics.
Enter n and r
Combinations C(n,r): order does NOT matter. Permutations P(n,r): order matters.
Standard mathematical formulas. Instant in-browser calculation, no account. Exact results, big numbers computed precisely.
In combinations the order does not matter; in permutations it does. Both are computed from factorials:
In a 6/49 lottery: C(49, 6) = 13,983,816 combinations. To choose 2 of 5: C(5,2) = 10, P(5,2) = 20.
In combinations the order does NOT matter (a group of people); in permutations the order matters (a ranking or a password).
C(n, r) = n! ÷ (r! × (n−r)!). For example, C(5, 2) = 10 ways to choose 2 out of 5.
P(n, r) = n! ÷ (n−r)!. For example, P(5, 2) = 20 ways to arrange 2 of 5 (order matters).
C(49, 6) = 13,983,816 possible combinations. The chance of the jackpot is 1 in almost 14 million.
Combinations when you select without regard to order (a poker hand); permutations when order matters (podium places).
C(5, 2) = 10 if order does not matter, or P(5, 2) = 20 if order matters.
An arrangement of r items from n is a partial permutation — you pick r items and put them in order. It is written P(n, r).
Lotteries, passwords and codes, forming teams, menus, probability and statistical analysis.