﻿ In math, a combination explains how many ways you can arrange a group from a larger group. The formula is...

Combinations, formula, practice & examples

Arrangements without Order

In math, a combination is an arrangement in which order does not matter. Often contrasted with permutations, which are ordered arrangements, a combination defines how many ways you could choose a group from a larger group.

Note: To understand this topic, it is highly advisable to be familiar with factorial notation .

The formula for combinations

To find all of the differennt ways to arrange r items out of n items. Use the combination formula below. (n stands for the total number of items; r stands for how many things you are choosing.)

Applied Example: Five people are in a club and three are going to be in the 'planning committee,' to determine how many different ways this committee can be created we use our combination formula as follows:

Point of Contrast: The committee is a common theme for combination problems because, often, it does not matter how your committee is arranged. In other words, it generally does not matter whether you think about your committee as Sue, John and Jimmy or as John, Sue and Jimmy. In either case, the same three people are in the committee. Contrast this with permutations and our example of a locker pass code. Unlike a committee, a pass code of a lock depends on the order which will dictate whether or not you can open up your lock!

Practice Problems: combinations

12C5 = (12)!/(5!×(12-5)!)=(12)!/(5!×(7)!)
(12×11×10×9×8×7!) /(5!×7!) = 792

Ultimate Math Solver (Free)

Free Algebra Solver ... type anything in there!