Combination Calculator
Calculate combinations (nCr) to find out how many ways you can choose items from a set.
Formula:
Result:
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.