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Combinatorics Calculator

Calculate factorials, permutations, and combinations with and without repetition. Uses BigInt for large numbers.

Factorial (n!)

Product of all positive integers up to n. Example: 5! = 120.

Permutations

Ordered arrangements. nPr = n!/(n-r)!. With repetition: n^r.

Combinations

Unordered selections. nCr = n!/(r!(n-r)!). With repetition: C(n+r-1, r).

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How to Use Combinatorics Calculator

Calculate permutations, combinations, and factorials. Solve counting problems with step-by-step explanations.

1

Select Calculation

Choose permutation, combination, or factorial from the available options.

2

Enter Values

Input n and r values for permutations and combinations, or n for factorials.

3

Calculate

Click calculate to see the result along with the formula and solution steps.

Common Use Cases

Probability Problems

Calculate the number of possible outcomes for probability and statistics exercises.

Contest Mathematics

Solve combinatorics problems commonly found in math competitions and olympiads.

Planning Arrangements

Determine possible seating arrangements, team selections, or schedule combinations.

Pro Tips

  • -Use combinations when order does not matter and permutations when it does.
  • -Factorials grow very fast so results for large numbers can be enormous.
  • -Remember: C(n,r) = n! / (r! * (n-r)!) for combinations formula.