Choosing a committee
Input
n = 10 people, r = 3 seatsOutput
10C3 = 120 committeesOrder of the three members does not matter—only who is on the committee.
10C3 = 120
Count unordered ways to choose r items from n using nCr = n!/(r!(n−r)!)—calculated locally in your browser. Compare with permutations when order matters.
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A combination calculator counts unordered selections: nCr = n! / (r!(n−r)!)—how many ways to choose r items from n when order does not matter.
Uses exact integer arithmetic for nCr when n ≤ 500 and 0 ≤ r ≤ n.
10C3 = 120
Combinations answer counting questions where order is irrelevant: lottery lines, committees, card hands, and sample subsets. The binomial coefficient nCr (also written C(n,r) or "n choose r") equals n factorial divided by r factorial times (n−r) factorial.
Contrast with permutations nPr = n!/(n−r)!, which count ordered arrangements (PIN codes, race podiums). If choosing {A,B} is the same as {B,A}, use nCr; if ABC differs from CBA, use nPr.
EverydayTools computes nCr with arbitrary-precision integers in your browser for n up to 500—inputs stay on your device.
Use nCr when order does not matter; use nPr when order matters.
n is the total number of distinct items or trials in the pool (non-negative integer).
r is how many items you choose at once; require 0 ≤ r ≤ n.
The tool displays nCr = n!/(r!(n−r)!) using big integers—for example 10C3 = 120.
If order matters (rankings, passwords), use the permutation calculator for nPr instead.
Input
n = 10 people, r = 3 seatsOutput
10C3 = 120 committeesOrder of the three members does not matter—only who is on the committee.
Input
n = 52 cards, r = 5Output
52C5 = 2,598,960 handsStandard count of unordered 5-card deals from a full deck.
Common real-world scenarios where this tool saves time.
Verify nCr by hand or calculator before submitting counting exercises.
Count possible unordered ticket combinations or loot pools.
Determine how many subsets of size r exist from a population of n.
| Tool | Formula | Order matters? | Example |
|---|---|---|---|
| Combination (nCr) | n!/(r!(n−r)!) | No | 10C3 = 120 committees |
| Permutation (nPr) | n!/(n−r)! | Yes | 10P3 = 720 lineups |
| Probability calculator | P(A), P(A∩B) | N/A | Chance of independent events |
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nCr (n choose r) counts unordered selections: nCr = n! / (r!(n−r)!). Example: 5C2 = 10 ways to pick 2 items from 5.
Use nCr when order does not matter (choosing a committee). Use nPr when order matters (podium places, PIN digits).
By convention, 0C0 = 1 (one way to choose nothing from nothing). The tool follows standard combinatorial definitions for edge cases.
Factorials grow extremely fast; n > 500 can exceed practical browser memory for exact integer arithmetic. Use smaller n or specialized software for huge values.
This tool counts arrangements (how many ways). The probability calculator computes event likelihoods between 0 and 1 for independent events.
Combination Calculator — nCr (n Choose r) (/combination-calculator) runs in your browser when supported—inputs are not uploaded to EverydayTools servers.
Uses exact integer arithmetic for nCr when n ≤ 500 and 0 ≤ r ≤ n.
Educational combinatorics aid—not a substitute for formal statistical consulting.
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Reviewed by EverydayTools Editorial Team on 2026-05-20.