Combination without Repetition Calculator
Determine the number of ways to select k distinct items from n without repetition or order dependence.
C(n, k): 210
How to Use This Calculator
- Enter the total number of items n.
- Specify how many items k you want to select without repetition.
- Read the computed binomial coefficient C(n, k).
- Apply the result to combinatorial, probability, or counting problems.
Formula
C(n, k) = n! / (k!(n − k)!)
Alternative recursive: C(n, k) = C(n − 1, k − 1) + C(n − 1, k)
Symmetry: C(n, k) = C(n, n − k)
Full Description
Combinations count selections where order does not matter and each item can be chosen at most once. They underpin probability problems ranging from lottery odds to sampling without replacement.
Frequently Asked Questions
What if k = 0 or k = n?
C(n, 0) and C(n, n) both equal 1, reflecting all-or-none selections.
How do I handle large numbers?
The calculator uses multiplicative formulas that minimize overflow, but extremely large n may exceed JavaScript bounds.
Is repetition allowed?
No. For combinations with repetition, use the stars-and-bars formula instead.
Can I use decimals?
C(n, k) is defined for integers with 0 ≤ k ≤ n. Inputs are rounded to the nearest integers.