Combination Calculator (nCr)

Understanding Combinations (nCr)

Combinations, denoted as nCr or C(n, r), represent the number of ways to choose 'r' items from a set of 'n' distinct items where the order of selection does not matter. It's a fundamental concept in combinatorics and probability theory.

The formula to calculate combinations is: $$C(n, r) = \frac{n!}{r!(n-r)!}$$ where 'n!' (n factorial) is the product of all positive integers up to n, 'r!' is the factorial of r, and '(n-r)!' is the factorial of (n-r).

Example: Suppose you have 5 fruits (n=5) and you want to choose 3 (r=3) to make a salad. The combination calculator helps you find out how many different groups of 3 fruits you can select, without considering the order in which you pick them.

This tool is useful in various fields like probability calculations, statistics, and any scenario where you need to determine the number of possible selections from a larger set.