Combination calculator
Calculator
The calculator needs JavaScript. The tables below give the same numbers for common cases.
How it is worked out
- nCr = n! ÷ (r! × (n − r)!) = 10! ÷ (3! × 7!).
- Equivalent: nPr ÷ r! = 120.
| Inputs | Answer |
|---|---|
| n: 10; r: 3 | C(10, 3) = 120. |
| n: 52; r: 5 | C(52, 5) = 2,598,960. |
| n: 49; r: 6 | C(49, 6) = 13,983,816. |
How to use it
A combination counts the ways to choose r items from n different items when order does not matter: nCr = n! ÷ (r! × (n − r)!). Choosing A and B is the same as choosing B and A.
For 10 items taken 3 at a time, 10C3 = 120. The number of 5-card hands from a 52-card deck is 52C5 = 2,598,960.
Frequently asked questions
What is 10C3?
120.
How many 5-card poker hands are there?
52C5 = 2,598,960.
How are nCr and nPr related?
nCr = nPr ÷ r!, because each group of r items can be ordered in r! ways.
Method: standard arithmetic shown step by step; no outside data is used. Checked 2026-11-12.
Written by Calculators Free Editorial Team · Data checked 2026-11-12
About · How we verify this · Editorial policy · Corrections
About · How we verify this · Editorial policy · Corrections
General information only. Results are plain arithmetic on the numbers you enter; check anything important (money, health, school work) against your own records or the official source.