統計学
Combination Calculator - Calculate Combinations Easily
Calculate combinations (nCr) quickly and easily with our online Combination Calculator. Understand combinations, formulas, and use cases for probability and combinatorics.
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Understanding Combinations
In combinatorics, a combination is a selection of items from a set where the order of selection does not matter. The formula for combinations, denoted as C(n, r) or $\(\binom{n}{r}\)$, calculates the number of ways to choose r items from a set of n distinct items.
The formula is given by:
$$C(n, r) = rac{n!}{r!(n - r)!}$$
Where:
- n is the total number of items in the set.
- r is the number of items to choose from the set.
- ! denotes the factorial operation, meaning the product of all positive integers up to that number (e.g., 5! = 5 × 4 × 3 × 2 × 1 = 120).
Combinations are widely used in probability, statistics, and computer science to solve problems involving selections and groupings, such as calculating probabilities in lottery games, forming teams, or selecting subsets of data.