# Tree Diagrams and The Counting Principle

Students learn that a tree diagram shows all the possible outcomes of a situation. For example, a tree diagram can be used to show all the possible outcomes of choosing a small, medium, large, or extra large t-shirt in red or blue. Note that the first level of the tree would be the 4 different sizes, and the second level of the tree would be the 2 different colors for each size, so there are 8 possible outcomes. Students also learn the Counting Principle, which states that when one item is selected from each of two or more sets, the total number of possible outcomes is equal to the product of the number of items in each set. For example, in the t-shirt problem above, the two sets are size and color, and since there are 4 possible sizes and 2 possible colors, the total number of possible outcomes is 4 times 2, or 8.