Combination Calculator
Compute combinations C(n,r), list every subset, and show the formula
📐 组合数 C(n, r)
💡 公式：C(n, r) = n! / (r! × (n-r)!)，表示从 n 个不同元素中取 r 个的组合数（不考虑顺序）
About this tool
The combination calculator counts subsets and can list them all:
- Count: enter n and r to compute C(n,r) = n!/(r!(n-r)!) with the formula and working shown
- List all: enter a set of items and generate every r-item subset
- Total: the number of combinations is displayed
- Large numbers: BigInt keeps big combinations exact
Combination formula
Choosing r items from n distinct items without regard to order gives C(n,r) = n! / (r! times (n-r)!). The difference from permutations is that order does not matter.
When to use it
- Probability, such as lottery odds
- Combinatorics
- Counting ways to choose a subset from a list
- Math homework help
Formula notes
- Combinations: C(n,r) = n! / (r! times (n-r)!), order ignored
- Symmetry: C(n,r) = C(n, n-r), so C(10,3) = C(10,7)
- Versus permutations: C(n,r) = A(n,r) / r!
- Pascal triangle: C(n,r) = C(n-1,r-1) + C(n-1,r)