We are building our own sandwich and we want to represent the sample space of all possible sandwiches by making a tree diagram. The sample space of an experiment is the set of all possible outcomes. In this case, the sample space is the result of two options.
Bread — wheat, sourdough, or multi-grain
Type of Sandwich — ham, turkey, steak, and chicken
Keep in mind that there are several ways to make a tree diagram. The part that matters most is that the sample space ends up with all of the possible combinations. Let's draw a tree diagram to represent the situation by pairing each type of bread with each type of sandwich.
There are 12 different outcomes in the sample space, so there are 12 different sandwiches possible.
