About this calculator
Answers are exact even when they run to many digits.
How to use it
- Enter n and r.
- Choose whether repetition is allowed.
- Read the number of selections.
The formula
nCr = n! ÷ (r! × (n − r)!); with repetition: (n + r − 1)Cr
- n
- items available
- r
- items chosen
Worked example
A 5-card hand from a 52-card deck
- 52C5 = 52! ÷ (5! × 47!) = 25,98,960.
What the result means
nCr = nC(n − r): choosing 3 of 10 to include is the same as choosing 7 to leave out.
Assumptions
- Items are distinct.
Limitations
- n up to 1,00,000 and r up to 20,000.
Frequently asked questions
What is the difference between permutation and combination?
Permutations count arrangements, where order matters. Combinations count selections, where order does not. ABC and CBA are two permutations but one combination.
What is 0!?
1, by definition. So nP0 = nC0 = 1.
How many ways can I choose 11 players from 15?
15C11 = 1,365.
Last reviewed on 6 October 2026. Found a mistake? Tell us.