Statistics Tool

Combinations Calculator (nCr)

Calculate the number of ways to choose a subset of items where order does not matter.

Σ The Formula

nCr = n! / [r! (n - r)!]

Real World Examples

Lottery
Choosing 6 numbers out of 49 → 13,983,816 combinations
Committee
Picking 3 people out of a group of 10 → 120 ways

# About This Calculator

A Combination is a selection of items from a larger set where the order of selection is irrelevant. This is what distinguishes it from a *Permutation*, where order is critical.

The notation nCr (also written as C(n, r) or as a binomial coefficient) represents the number of ways to pick r unique elements from a pool of n. It is the foundation of probability and statistics, particularly in binomial distributions.

How To Use

  1. Enter the **Total Number of Items (n)**.
  2. Enter the **Number of Items to Choose (r)**.
  3. The tool will calculate the total number of unique combinations possible.
  4. Note: $r$ cannot be larger than $n$.

Frequently Asked Questions

What's the difference between nCr and nPr?+

In nCr (Combinations), picking {'{A, B}'} is the same as picking {'{B, A}'}. In nPr (Permutations), they are counted as two different arrangements. Combinations are always less than or equal to permutations.

Is 0! really 1?+

Yes, in mathematics, 0 factorial is defined as 1. This ensures that the combinations formula works correctly for cases like choosing 0 items (there is only 1 way: choose nothing).

Is Combinations Calculator (nCr) free to use?+

Yes, Combinations Calculator (nCr) on Matheric is completely free to use. We believe in accessible education and utility for everyone.

How accurate is Combinations Calculator (nCr)?+

We use standard mathematical formulas and high-precision computing algorithms to ensure results for Combinations Calculator (nCr) are accurate for academic and professional use.

Can I use Combinations Calculator (nCr) on my phone?+

Yes! Combinations Calculator (nCr) is fully responsive and optimized for all devices, including smartphones, tablets, and desktops.

Do you save my data?+

No. We prioritize your privacy. All calculations are performed in your browser or temporarily processed, and we do not store your personal input data.

About

A Combination is a selection of items from a larger set where the order of selection is irrelevant. This is what distinguishes it from a *Permutation*, where order is critical.

The notation nCr (also written as C(n, r) or as a binomial coefficient) represents the number of ways to pick r unique elements from a pool of n. It is the foundation of probability and statistics, particularly in binomial distributions.

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