Combination Calculator
Enter n and r below to instantly get both the combination (nCr) and permutation (nPr).
Combinations vs. Permutations
Both count ways to choose r items from a set of n. The only difference is whether order matters: combinations don't care about order, permutations do.
Worked example
Choose 3 people from a group of 10.
nCr = 10! / (3! × 7!) = 120 ways, if order doesn't matter
nPr = 10! / 7! = 720 ways, if order matters (like assigning 1st, 2nd, and 3rd place)
Keep going
- Combinations and permutations are built entirely from factorials; the factorial calculator shows that building block on its own. Factorial Calculator
- Combinations count how many ways an outcome can happen; the probability calculator turns that count into an actual probability once you know the total outcomes. Probability Calculator
Frequently Asked Questions
What is the difference between a combination and a permutation?
A combination counts ways to choose r items from n where order doesn't matter (picking a 3-person committee). A permutation counts ways where order does matter (ranking 1st, 2nd, and 3rd place). Permutations are always greater than or equal to combinations for the same n and r.
What is the formula for nCr?
nCr = n! / (r! × (n − r)!), where n! means n factorial (n × (n−1) × ... × 1).
What is the formula for nPr?
nPr = n! / (n − r)!. It's the same idea as combinations, but without dividing out the r! ways to arrange the chosen items, since order matters here.
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