Combination Calculator – Guide & Formulas
Calculate combinations (nCr) where the order of selection does not matter. Ideal for lottery odds, team selections, and probability audits.
Quickly solve combinations (nCr) for groups where ordering is irrelevant. Highly valuable for games of chance, random team divisions, committee planning, and statistics studies.
Key Takeaway
Use the free Combination Calculator to calculate combinations (ncr) where the order of selection does not matter. ideal for lottery odds, team selections, and probability audits. Get instant results with step-by-step explanations.
How to Use the Combination Calculator
- Enter the total population size (n) in the first field.
- Enter the sample selection size (r) in the second field.
- Review the calculated binomial coefficient and the mathematical steps.
- Copy the combination details instantly.
The Formula
Variable Definitions
- n: Total number of items in the population pool
- r: Number of items selected for the group
- nCr: Number of unique combinations
Selecting a 3-Person Team
A manager must select a team of 3 employees from a group of 8 candidate workers.
- Step 1: Set n = 8 and r = 3.
- Step 2: Apply formula: 8! / (3! * 5!).
- Step 3: 8! / 5! = 8 * 7 * 6 = 336.
- Step 4: Divide by 3! (6) = 56 unique teams.
Frequently Asked Questions
What is the main difference between permutations and combinations?
In permutations, the order of elements matters. In combinations, order does not matter. For example, {A, B} and {B, A} represent two permutations, but only one combination.
What is the formula for combinations with repetition?
The formula is (n + r - 1)! / (r! * (n - 1)!).
Why is nCr often called the binomial coefficient?
Because the coefficients of the expanded binomial (x + y)^n correspond exactly to the combination values C(n, r).