Combination Calculator
Calculate the number of unordered combinations—commonly referred to as "n choose r"—to select subsets from a group where the internal sequence or arrangement of items does not matter.
Total distinct objects to choose from
Number of elements selected into the group
Total possible unique subsets regardless of sequence
How to Use This Calculator
- Enter the total pool size (n).
- Enter the number of items to select into the team or hand (r).
- Inspect the resulting binomial coefficient and contrast with ordered permutations.
Formula & Calculation Methodology
Combinations divide total permutations by r! to neutralize the duplicate permutations arising from different arrangements of the same chosen elements.
Worked Example
Selecting a committee of 4 from 10 members
Dealing a 5-card poker hand from 52 cards
Frequently Asked Questions
Why is nCr symmetric (nCr = nC(n-r))?↓
Choosing r items to include in a group is mathematically identical to choosing the remaining (n - r) items to exclude.
What is the relationship between nCr and Pascal’s Triangle?↓
Every entry in Pascal’s Triangle corresponds to a binomial coefficient nCr, where n is row number and r is column index.
How does nCr differ from nPr?↓
In combinations (nCr), order does not matter ({A, B} is the same as {B, A}). In permutations (nPr), order matters.
What is a limitation of standard combination counting?↓
Standard nCr assumes items are not replaced and all items in the initial pool are completely distinct from one another.
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Source Citation & Disclaimer
Informational tool only; not licensed tax, legal, or financial advice.