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Combination Formula Calculator

Online combination: choose m of n elements without regard to order, C(n,m)=n!/(m!(n−m)!).

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C(n,m)=n!/(m!(n−m)!)
Total
0≤m≤n

📖 Tutorial | Combination

1. Definition
Choosing m of n distinct elements without regard to order gives C(n,m)=n!/(m!(n−m)!).
2. Formula & Notation
C(n,m)Combinations
3. Properties & Laws
  • Unordered;
  • Symmetric C(n,m)=C(n,n−m);
  • C(n,0)=C(n,n)=1;
  • P(n,m)=C(n,m)·m!.
4. Steps
  1. Enter n,m;
  2. Click "Calculate";
  3. Or click "Load Example".
5. Worked Examples
Example: C(5,3)=5!/(3!·2!)=10.
6. Common Pitfalls
Unordered;
Denominator includes m!;
Use symmetry.

❓ FAQ | Combination

Combination?
Unordered.
Formula?
n!/(m!(n−m)!).
Symmetric?
Yes.
Vs permutation?
m! factor.
Example?
10.
m=0?
1.