# Section 8.2

## Combinations

In Section 8.1, we used permutations to count different arrangements of objects. The word “arrangements” is used since different orders of objects must be counted separately. Different arrangements of numbers and letters on an auto license plate lead to different license plate numbers.

In many applications, different arrangements of objects are not counted differently. Many states have lotteries that are used to fund schools and environmental causes. In these lotteries, lottery officials select numbered balls from a group of balls labeled 1 through a larger number like 52. A player wins the lottery jackpot if the numbers the player selects matches the numbers on the balls selected by officials. The order in which the balls are drawn does not have to be duplicated. The number of ways the balls can be selected from a larger group of balls is calculated using combinations. In combinations, groupings of objects are counted and the order of the objects in the grouping are irrelevant.