🔢 Combination Calculator (nCr)
Calculate the number of ways to choose r items from n objects where order doesn't matter. Perfect for lottery calculations, team selections, and probability problems.
Input Values
Total number of items to choose from (0-1000)
Number of items to select (r ≤ n)
Quick Examples
Results
Combination Result
120
C(10,3) = 120
Formula Used
C(n,r) = n! / (r! × (n-r)!)
Related Information
Corresponding Permutation (nPr): 720
Binomial Coefficient: (10 choose 3)
Input Error
Calculation Steps
All Possible Combinations
Frequently Asked Questions
A combination calculator computes nCr, which represents the number of ways to choose r items from n total items where the order doesn't matter. It's also known as the binomial coefficient or "n choose r".
Combinations (nCr) don't consider order - choosing items A, B, C is the same as choosing C, B, A. Permutations (nPr) do consider order - ABC and CBA are different arrangements.
The combination formula is: nCr = n! / (r! × (n-r)!), where n is the total number of items, r is the number of items to choose, and ! represents factorial.
Combinations are used in lottery calculations, team selections, menu choices, card games, and any situation where you need to select a subset without caring about order.
C(52,5) means choosing 5 cards from a standard 52-card deck, which equals 2,598,960 different possible hands in poker.
No, you cannot choose more items (r) than the total available items (n). The calculator will show an error if r > n.
There is exactly one way to choose nothing from any set - by choosing no items at all. This is a fundamental principle in combinatorics.
For large numbers, use the multiplicative formula: C(n,r) = (n×(n-1)×...×(n-r+1)) / (r×(r-1)×...×1), or take advantage of the symmetry C(n,r) = C(n,n-r).
Disclaimer
This combination calculator is provided for educational and informational purposes only. While we strive for accuracy, please verify important calculations independently. The results should not be used as the sole basis for critical decisions.