🔀 Permutation and Combination Calculator
Permutations count arrangements where order matters — gold, silver, bronze medals for 5 runners is P(5,3) = 60. Combinations count groups where order does not matter — choosing any 3 of 5 friends is C(5,3) = 10.
The calculator builds both with direct multiplication instead of giant factorials, so it stays exact for n all the way up to 170.
How to use this calculator
Enter n for the total items and r for how many you choose. The calculator returns both P(n,r) and C(n,r) at once.
- Type n, the total number of items to choose from.
- Type r, how many items are chosen or arranged.
- Make sure r is not larger than n.
- Press Calculate and read the permutation count and the combination count.
Frequently asked questions
What does this calculator compute?
It computes P(n,r), the number of ordered arrangements of r items chosen from n, and C(n,r), the number of unordered groups. Both are built by direct multiplication, exact for n up to 170.
Can you show a worked example?
With n = 5 and r = 3, P(5,3) = 60 ordered arrangements and C(5,3) = 10 unordered groups. Medal positions among 5 runners use 60; picking any 3 friends from 5 uses 10.
What is the difference between permutations and combinations?
Order matters in permutations and does not in combinations. Arranging 3 books on a shelf is a permutation problem; choosing 3 books to borrow is a combination problem, and its count is always smaller.
Why is there a maximum n of 170?
Beyond 170 the factorial-style products exceed what standard floating point numbers can hold, so results would lose exactness. Real counting problems rarely need larger values, and the cap keeps every answer precise.