Combinations & Permutations Calculator
Everyday
Combinations (nCr) count how many ways you can choose r items from n when order does not matter; permutations (nPr) count them when order does matter. This calculator also gives the with-repetition variants and the underlying factorials. Every result is computed with arbitrary-precision integers, so even huge values like C(100, 50) are exact — no rounding or scientific-notation loss. Handy for probability, lottery and card odds, password-space sizing, and combinatorics homework.
n! / (r! · (n−r)!)
10
Order doesn't matter
n! / (n−r)!
20
Order matters
(n+r−1)! / (r! · (n−1)!)
15
Repeats allowed, order ignored
nʳ
25
Repeats allowed, order matters (nʳ)
n!
120
r!
2
(n−r)!
6
Values are capped at 10,000 to stay instant. All math is exact (arbitrary precision).
How to use
- Enter n — the total number of items to choose from.
- Enter r — how many you pick.
- Read off combinations (order ignored) and permutations (order matters), plus the repetition variants and factorials. Copy any exact value.
Frequently asked questions
- What is the difference between a combination and a permutation?
- Order. A combination counts selections where order does not matter (e.g. a lottery draw); a permutation counts arrangements where order matters (e.g. a podium of 1st/2nd/3rd).
- When do I use the with-repetition versions?
- When the same item can be picked more than once — like a 4-digit PIN (permutations with repetition, 10⁴) or scoops of ice cream where flavours can repeat (combinations with repetition).
- Are the big numbers exact?
- Yes. Everything uses arbitrary-precision integers, so values with hundreds of digits stay exact instead of being rounded to floating point.
- Why is there a maximum of 10,000?
- It keeps the calculation instant in your browser. Larger factorials grow to hundreds of thousands of digits and would slow the page down.
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