A restaurant sells 4 kinds of sandwiches: turkey, roast beef, veggie, and ham. Customers have a choice of 3 types of bread: wheat, white, or rye. How many different sandwiches are possible?

## Prealgebra question

# 3 Answers

To find out how many different sandwiches are possible, we can visualize all of the sandwiches! I know there are three types of bread - wheat, white, and rye. I would make each of those a group, like this:

- Wheat
- White
- Rye

Now, for each type of bread, there are 4 choices of filling - turkey, roast beef, veggie, and ham. Let's add those to each group, like this:

- Wheat:

- Turkey on wheat
- Roast beef on wheat
- Veggie on wheat
- Ham on wheat

- White

- Turkey on white
- Roast beef on white
- Veggie on white
- Ham on white

- Rye

- Turkey on rye
- Roast beef on rye
- Veggie on rye
- Ham on rye

Now that we've laid out each possibility, we can count the different choices! Altogether, there are 12 different possibilities. We can also say that there are 3 types of bread, with 4 choices of filling for each - multiply 3 groups times 4 choices and that is 12!

Wheat White Rye

* Sandwich 1 * Sandwich 1 * Sandwich 1

* Sandwich 2 * Sandwich 2 * Sandwich 2

* Sandwich 3 * Sandwich 3 * Sandwich 3

* Sandwich 4 * Sandwich 4 * Sandwich 4

**Total of 12 sandwiches After visualizing, you can see the math - 4 x 3 = 12**

For each bread type there are 4 choices of sandwich. So for wheat bread there are 4 possible sandwiches, white bread has 4 possible sandwiches and rye bread has 4 possible sandwiches. 4+4+4=12 or 4*3=12