About Combinations (nCr)
In probability theory, a Combination calculates the number of ways to select items from a group, where the order of selection does NOT matter. This is the math of Lotteries, Poker hands, and committee selections.
The "Fruit Salad" Analogy
If you are making a fruit salad with Apples, Bananas, and Grapes, it doesn't matter which one you put in the bowl first. The resulting group is the same. Apple-Banana-Grape is identical to Grape-Apple-Banana. This is a Combination.
The Formula: nCr
C(n, r) = n! / (r! * (n - r)!)
It divides the Permutation formula by r! to remove the duplicate orderings.
Example: The Lottery
In a 6/49 lottery, you must choose 6 numbers from 49. Order doesn't matter.
C(49, 6) = 13,983,816.
This means you have a 1 in ~14 million chance of winning. This tool reveals just how vast the possibilities are.
How to Use
Enter the Total Pool (n) and the number to Choose (r). The tool calculates the distinct groups.