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Prealgebra question

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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:
    1. Turkey on wheat
    2. Roast beef on wheat
    3. Veggie on wheat
    4. Ham on wheat
  • White
    1. Turkey on white
    2. Roast beef on white
    3. Veggie on white
    4. Ham on white
  • Rye
    1. Turkey on rye
    2. Roast beef on rye
    3. Veggie on rye
    4. 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