# Combination Calculator Calculate combinations (nCr) instantly with step-by-step work, with or without repetition. Perfect for lottery odds, poker hands, and team selection. --- - **Canonical URL:** https://dothecalculation.com/calculators/combination-calculator - **Category:** Math calculators - **Publisher:** Do The Calculation (https://dothecalculation.com) - **Cost:** Free, no account or sign-up required - **Privacy:** Runs entirely in the browser; inputs are never sent to a server - **Methodology:** https://dothecalculation.com/methodology --- ## Related Calculators Combinations show up constantly in card-game probability — the [poker odds & outs calculator](/calculators/poker-odds-calculator) uses the same nCr math behind the scenes to compute exact hypergeometric probabilities for completing a drawing hand, rather than the quick 'outs times 4 or 2' table shortcut. ## Frequently asked questions ### What is a combination calculator? A combination calculator finds the number of ways to choose r items from n distinct items where order doesn't matter. ### What is the combination formula? The combination formula is nCr = n! / (r!(n-r)!). This is also known as the nCr combination formula. ### What is the difference between combination and permutation? In combinations, order doesn't matter (selections). In permutations, order matters (arrangements). ### When do I use combinations? Use combinations when the order of items doesn't matter, such as lottery numbers, choosing a team, or picking toppings. ### What is n choose k? "n choose k" is another name for combinations. It means choosing k items from n items. ### What is the relationship between combinations and permutations? nCr = nPr / r!. Combinations are smaller because order doesn't matter. ### How do I calculate combinations? To calculate combinations: identify n and r, use the formula nCr = n!/(r!(n-r)!), and calculate. ### What is 0!? 0! = 1 (mathematical convention). ### Can I use combinations with repetition? Yes — toggle "Allow repetition" in the calculator. The formula becomes C(n+r-1, r) = (n+r-1)! / (r!(n-1)!). ### What is the difference between nCr and nPr? nCr (combinations) is for selections where order doesn't matter. nPr (permutations) is for arrangements where order matters. ### How many ways to choose 3 from 10? 10C3 = (10 × 9 × 8) / (3 × 2 × 1) = 120 ways. ### How many 5-card poker hands are possible? 52C5 = 2,598,960 possible poker hands. ### How many ways to choose 2 toppings from 8? 8C2 = (8 × 7) / (2 × 1) = 28 ways. ### What is a binomial coefficient? The binomial coefficient is another name for combinations. It's the number of ways to choose r items from n items. ### Is this combination calculator free? Yes — completely free with no registration required. ## Related guides - [Standard Deviation Guide: Measure Data Spread Clearly](https://dothecalculation.com/blog/math/standard-deviation-explained) — Understand variance, population vs sample formulas, and data spread with worked examples tied to the live DTC standard deviation calculator. - [Random Number Generation Guide: Seeded PRNGs, True Randomness, and Safe Use Cases](https://dothecalculation.com/blog/math/random-number-generation) — Learn the difference between deterministic seeded generators, browser pseudo-random functions, and cryptographically strong randomness so you can use the right tool for the job. ## Related calculators - [Permutation Calculator](https://dothecalculation.com/calculators/permutation-calculator) — Calculate permutations (nPr) and combinations (nCr) instantly with step-by-step work. 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