Permutation and Combination Calculator (nPr, nCr)
A permutation (nPr) counts the number of ways to arrange r items out of n where order matters, while a combination (nCr) counts the number of ways to choose r items out of n where order does not matter. Toolverge computes both from the same n and r using exact BigInt factorial ratios, so results stay precise even for larger n where a normal number would lose accuracy.
How it works
- Enter n (total items) and r (items chosen).
- nPr and nCr are computed from exact BigInt factorial ratios.
- Both results are shown together, since they answer related questions.
Formula nPr = n!/(n−r)!; nCr = n!/(r!(n−r)!)
Frequently asked questions
What is 5P2?
5P2 = 5!/(5−2)! = 20 — the number of ways to arrange 2 items chosen from 5 where order matters.
What is 5C2?
5C2 = 5!/(2!×3!) = 10 — the number of ways to choose 2 items from 5 where order does not matter.
What is the difference between permutation and combination?
Permutations count arrangements where order matters; combinations count selections where order does not matter.
What happens when r equals n?
nPr equals n! (every arrangement of all items) and nCr equals 1 (there is only one way to choose all of them).
What happens when r is 0?
Both nPr and nCr equal 1 — there is exactly one way to choose nothing.