Combination Calculator
Compute nCr = n! ÷ (r!(n − r)!): how many unordered groups of r from n.
Calculator
Use the Combination Calculator
Result
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Formula
nCr = n! ÷ (r! × (n − r)!)
Step-by-step
- 1
Enter n and r
n is the pool size, r is the group size.
- 2
Read the count
Unordered selections are shown.
Worked example
Example input: n: 10, r: 3
Result: 120
Related tools
- Permutation Calculator
Ordered arrangements.
Frequently asked questions
What does 10 choose 3 mean?
120 — the number of ways to pick 3 items out of 10 when order is irrelevant, as {1, 2, 3} counts the same as {3, 1, 2}. Enter 10 and 3 above and the calculator returns 120. Lottery-style picks, teams, and committee selections all follow this same count.
How is C(n, r) different from P(n, r)?
Permutations count arrangements, combinations count selections: 10P3 is 720 because the same three items have 6 internal orders, and 720 divided by 6 lands at 120.
What do C(n, 0) and C(n, n) return?
Both return 1: there is exactly one way to pick nothing, and exactly one way to pick everything. Order-dependent edge cases like r greater than n have none, so the answer is nothing.