By Zencalcy Editorial TeamLast reviewed About us
Count how many unordered groups of r items can be chosen from n — lottery odds, poker hands, committees. The nCr formula is displayed with every answer.
Unordered selections nCr with the factorial formula shown.
C(n,r) = n! / (r! · (n−r)!)
| Symbol | Meaning |
|---|---|
| n | Total items available |
| r | Items chosen (order ignored) |
C(52,5) = 2,598,960 possible 5-card poker hands. C(10,3) = 120 committees of 3 from 10 people.
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Combinations ignore order (hand of cards); permutations count order (race finish). Use nCr here, nPr for ordered.
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Content updated: September 2026