So the main use of Venn Diagrams is to visualize simple examples as a way of getting your brain working well enough to understand more complex groupings of data. From a theoretical standpoint, it's what comes next that is more important. But Venn Diagrams provide a useful introduction that sets the stage for the multiplication principle, combinations, and permutations which are the topics on the horizon.

### Venn Diagrams

In your homework you've been working with Venn Diagrams. These provide a nice way of visualizing groupings of data when you're splitting outcomes into only 2 or 3 categories. The reason this is restricted to no more than 3 groupings is that with 4 or more categories, there's not a simple 2-dimensional way to visualize all the possible overlappings. For instance, in a Venn Diagram with 3 sets, there are 8 different regions shown in your picture. (One of the 8 regions in the picture is the white region outside all the circles.) But if you had 4 sets instead of 3, there would be 16 regions, and there's no obvious way to draw 4 circles and display all the 16 sub regions.

So the main use of Venn Diagrams is to visualize simple examples as a way of getting your brain working well enough to understand more complex groupings of data. From a theoretical standpoint, it's what comes next that is more important. But Venn Diagrams provide a useful introduction that sets the stage for the multiplication principle, combinations, and permutations which are the topics on the horizon.

So the main use of Venn Diagrams is to visualize simple examples as a way of getting your brain working well enough to understand more complex groupings of data. From a theoretical standpoint, it's what comes next that is more important. But Venn Diagrams provide a useful introduction that sets the stage for the multiplication principle, combinations, and permutations which are the topics on the horizon.