Combinations Calculator

Calculate combinations (unordered selections). Free online nCr calculator.

The Combinations Calculator computes the number of ways to choose r items from n total items when order doesn't matter. Unlike permutations, ABC and BAC count as the same combination. This tool calculates nCr = n!/(r!(n-r)!) for any valid inputs. Essential for probability, lottery odds, and selection problems.

Common use cases

  • Lottery odds calculation
  • Team selection from a pool
  • Committee formation
  • Handshake problems
  • Subset counting

How to use

  1. Enter total items (n)
  2. Enter items to choose (r)
  3. Click calculate for nCr
  4. View the factorial calculation
  5. Compare with permutations if needed

FAQ

What is a combination?

An unordered selection of items. Choosing 3 from ABCD: ABC, ABD, ACD, BCD are the 4 combinations.

What is the formula?

C(n,r) = n!/(r!(n-r)!) where n is total items and r is items chosen.

Why divide by r!?

To remove duplicate orderings. Each combination corresponds to r! permutations.

What is Pascal's Triangle?

A triangular array where each entry is C(n,r). Used for binomial coefficients.