Permutation and Combination Calculator
Enter how many items there are and how many you are choosing. The calculator counts the ways to choose when order matters (permutations) and when it does not (combinations).
Type a number and the answer appears straight away.
Combinations (order does not matter)12010C3
- Permutations (order matters), 10P3
- 720
- Permutations with repeats allowed
- 1,000
- Combinations with repeats allowed
- 220
- 10! (ways to arrange all 10)
- 3,628,800
Use permutations when the order counts, as in a race finish or a PIN. Use combinations when it does not, as in a lottery draw or a hand of cards.
The math behind it: Permutations and Combinations
nPr = n! / (n - r)!; nCr = n! / (r! x (n - r)!)
Choosing 3 items from 10 can be done in 720 ordered ways (permutations) or 120 unordered ways (combinations). The combination count is smaller because each group of 3 can be arranged in 6 different orders, and 720 / 6 = 120.
Common questions
What is the difference between a permutation and a combination?
In a permutation the order matters; in a combination it does not. The podium finishers in a race are a permutation. The members picked for a committee are a combination.
How do I calculate combinations?
Use nCr = n! / (r! x (n - r)!). For 10 choose 3: 10 x 9 x 8 / (3 x 2 x 1) = 120.
How many 5-card hands are there in a deck of 52?
2,598,960. That is 52 choose 5, a combination because the order of the cards in your hand does not matter.
You might also need
Checked and updated: