What is the difference between permutations and combinations?

In permutations, order matters (ABC ≠ BAC). In combinations, order does not matter (ABC = BAC). There are always fewer combinations than permutations.

How do I calculate P(5,3)?

P(5,3) = 5! / (5-3)! = 120 / 2 = 60. This counts ordered arrangements of 3 items from 5.

How do I calculate C(5,3)?

C(5,3) = 5! / (3! × 2!) = 120 / 12 = 10. This counts unordered selections of 3 items from 5.

How many ways can you choose 6 lottery balls from 40?

C(40,6) = 3,838,380. A classic application of combinations.

📐 Probability Calculator

Calculate permutations P(n,r) and combinations C(n,r) by entering n and r. The calculator shows the formula and result. In permutations order matters; in combinations it does not.

C(n,r) = n! / (r! × (n-r)!)

Järjestämättömät valinnat — järjestys ei merkitse

Syötä arvot

n (alkioiden kokonaismäärä)r (valittujen määrä)

C(10,3) =

120