Combination Calculator
Calculate the number of combinations C(n, r), which is the number of ways to choose r items from a set of n items without regard to the order of selection.
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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 combination formula, denoted as C(n, r) or $$ \binom{n}{r} $$, calculates the number of possible combinations of choosing r items from a set of n distinct items.
The formula for combinations is: $$ C(n, r) = \frac{n!}{r!(n-r)!} $$ 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, which means the product of all positive integers up to that number (e.g., 5! = 5 × 4 × 3 × 2 × 1 = 120).
Combinations are used in probability, statistics, and various fields of mathematics to count the number of ways to select items without considering order. For example, if you want to know how many different groups of 3 students can be formed from a class of 20, you would use combinations.
Use this calculator to quickly find the number of combinations for your problems!