How to Calculate Combinations
What is Combinations?
Combinations count the number of ways to select k items from n items without regard to order. Written as C(n,k) or "n choose k", used in probability and statistics.
Formula
C(n,k) = n! / (k! × (n-k)!)
Step-by-Step Guide
- 1Enter n (total items) and k (items to select)
- 2Calculate factorials n!, k!, and (n-k)!
- 3Divide n! by the product of k! and (n-k)!
Worked Examples
Input
C(5,2)
Result
10
5! / (2! × 3!) = 120 / 12 = 10
Common Mistakes to Avoid
- ✕Confusing combinations with permutations
- ✕Incorrect factorial calculations
Ready to calculate? Try the free Combinations Calculator
Try it yourself →