Permutations and Combinations Calculator
Calculate permutations (nPr), combinations (nCr) and factorials.
Permutations and combinations count how many ways you can pick r items from a set of n. The difference is order: permutations (nPr) treat different arrangements as distinct, while combinations (nCr) do not. Enter n and r and this calculator returns both, along with the factorials that define them.
For example, picking 2 people from 5 gives 20 permutations (nPr) because first and second place are different, but only 10 combinations (nCr) because a pair is the same regardless of order. The formulas are nPr = n! / (n − r)! and nCr = nPr / r!, which is why the factorials are shown too.
How to use it
- 1Enter n, the total number of items to choose from.
- 2Enter r, how many you are selecting. It must be a whole number from 0 up to n.
- 3Read nCr for order-independent selections and nPr for ordered arrangements.
- 4Check n! and r! if you want the underlying factorial values.
Frequently asked questions
What is the difference between a permutation and a combination?+
A permutation counts arrangements where order matters, so AB and BA are two outcomes. A combination counts selections where order does not matter, so AB and BA are the same one outcome. That is why nPr is always greater than or equal to nCr.
How is nCr calculated?+
nCr equals n! divided by r! times (n − r)!. Equivalently, this tool computes the permutation nPr first, then divides by r!. For n = 5 and r = 2 that gives 20 ÷ 2 = 10 combinations.
Why does it say “too large”?+
Factorials grow extremely fast. Beyond 170! the result exceeds the largest number JavaScript can represent, so any output that overflows is shown as “too large” rather than an inaccurate figure.
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