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Combinatorics Calculator

Calculate permutations (nPr) and combinations (nCr) instantly for probability and statistics problems.

📐 Formulas

nPr = n! / (n-r)!

Order matters

nCr = n! / (r! × (n-r)!)

Order doesn't matter

n! = n × (n-1) × ... × 1

Factorial

🔢 Results will appear here

Enter n and r values, then click "Calculate"

This maths solver is essential for Probability Theory, Statistics Students, and Software Engineers (and for everyone else who needs to count possible arrangements or selections).

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Mastering Counting: Permutations and Combinations

Combinatorics is a branch of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. Our **Combinatorics Calculator** provides a precise **maths solver** for the two fundamental operations in this field: **Permutations** and **Combinations**.

Permutations (nPr): When Order Matters

A permutation is an arrangement of all or part of a set of objects, with regard to the order of the arrangement. For example, the arrangements (A, B) and (B, A) are considered different.

P(n, r) = n! / (n - r)!

Combinations (nCr): When Order Doesn't Matter

A combination is a selection of all or part of a set of objects, without regard to the order of the selection. For example, the selections {A, B} and {B, A} are considered the same.

C(n, r) = n! / [r! (n - r)!]

Real-World Applications

  • Lottery & Gaming: Calculating the odds of drawing a specific hand in poker (Combinations).
  • Computer Science: Determining the number of possible password arrangements (Permutations).
  • Logistics: Planning the most efficient route for a delivery truck with multiple stops (Permutations).
  • Genetics: Analyzing possible gene combinations in offspring (Combinations).

Combinatorics FAQ

What is a Factorial (!)?

A factorial is the product of all positive integers less than or equal to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.

When should I use nPr vs nCr?

Ask yourself: "Does the sequence matter?" If yes (like a door lock code), use Permutations. If no (like picking people for a committee), use Combinations.

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