Binomial Coefficient Calculator
Must be a non-negative integer
Must be between 0 and n
Result
How to Use
- Enter the total number of items (n)
- Enter the number of items to select (k)
- Click the "Calculate" button
- The binomial coefficient C(n,k) will be displayed
About Binomial Coefficients
The binomial coefficient C(n,k) represents the number of ways to choose k items from a set of n items.
Formula: C(n,k) = n! / (k! × (n-k)!)
Common applications:
- Probability calculations
- Combinatorics problems
- Pascal's triangle
- Binomial theorem
Common Examples
| n | k | C(n,k) | Meaning |
|---|---|---|---|
| 5 | 2 | 10 | Ways to choose 2 items from 5 |
| 6 | 3 | 20 | Ways to choose 3 items from 6 |
| 4 | 0 | 1 | Ways to choose 0 items from 4 |
| 7 | 7 | 1 | Ways to choose all 7 items |
Properties
- C(n,0) = C(n,n) = 1
- C(n,k) = C(n,n-k)
- C(n,k) = C(n-1,k) + C(n-1,k-1)
- Sum of C(n,k) for k=0 to n equals 2ⁿ
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