Combinations Calculator: Your Math Helper

What are combinations?

Combinations calculate how many ways you can choose items where order doesn't matter. For example, choosing 2 fruits from {apple, banana, orange} gives 3 combinations: {apple, banana}, {apple, orange}, {banana, orange}.

Combinations vs Permutations:

  • Combinations: Order doesn't matter (AB = BA)
  • Permutations: Order matters (AB ≠ BA)

Need permutations instead? Click here for permutations calculator

Input requirements:

  • Both n and r must be non-negative integers
  • r cannot be greater than n (can't choose more items than available)
  • Maximum recommended value: 170 (to avoid overflow)

Welcome. This combinations calculator helps count ways to choose items. Use it even if math feels hard.

How It Works

The calculator uses the formula: n! / (r! × (n - r)!). You enter two numbers. It then shows the result with detailed calculation steps.

Step-by-Step Instructions

Understanding the Input Fields

The first input (n) asks for the total number of items. Use a non-negative whole number.

The second input (r) asks for how many items to choose. r must be a non-negative whole number and cannot be larger than n.

The tool limits n to 170 to avoid overflow issues.

Interpreting the Output

The result shows the number of combinations calculated based on your inputs. It also details the calculation steps:

This helps you follow the math behind the answer.

Combinations vs Permutations

In combinations, order does not matter, so AB equals BA. In permutations, order matters, so AB does not equal BA. If you need the permutations calculator, click here.

Tool Limitations and Special Notes

The tool checks for valid input. It warns if a field is empty or if r is greater than n. Negative numbers are not accepted.

Common Use Cases

This calculator helps when forming committees or teams. It can be used for event planning or any scenario where counting choices is needed.

Try it now and see how easy it is to do the math.