Calculate the number of unordered combinations (nCr) of selecting r items from n choices.
Result
Order does not matter in combinations.
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nCr = n! / [r! × (n - r)!]
n = 10 items, choose r = 4.
10C4 = 210 unique unordered combinations.
Find the number of ordered arrangements (permutations) of r elements from n total items.
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Open calculatorIn mathematics, 'n choose r' (nCr) represents the number of ways to pick r unordered outcomes from a pool of n distinct possibilities.
Choosing r items to include is mathematically identical to choosing (n - r) items to exclude, producing identical binomial coefficient values.
Combinations describe the coefficients in the Binomial Theorem $(x+y)^n$ and form the rows of Pascal's Triangle. They are ubiquitous in card game probabilities, lottery analyses, and statistical sampling.