To keep track of which and how many combinations exist, it can be useful to use a counting model.

Tree diagram

A tree diagram is a model that provides an overview of the number of combinations.

The tree diagram works in such a way that each time you have a possible outcome, you draw a branch. When the tree diagram is completed, you count the number of endpoints on the tree and thereby find the result of the problem.

Example: What possible outcomes are there when you “flip a coin” with 2 coins 

A good place to create tree diagrams is at Counting Tree (dynamic)

Matrix

Another way to create a model of combinations is a matrix. A matrix is a table arrangement with two dimensions. In some cases, it is advantageous to use a matrix because the possible combinations are easier to read, since they appear directly in the matrix, unlike in a tree diagram. However, a matrix also has the limitation that it can only work in two dimensions. Thus, one can create a matrix for two dice throws, but not for three or more dice.

Example: Matrix for two coin tosses (this example is with replacement)

From both the tree diagram and the matrix, one can see that there are 4 possible outcomes (heads–heads, heads–tails, tails–heads, and tails–tails).

This means, for example, that there are 3 possibilities out of the 4 where there is at least one heads.