Sandwiches

Have you ever wondered how many unique subway sandwiches you can make? Today we are going to find out.

Start with the bread

According to the subway website, you have six types of bread to pick from:

This gives us 6 options to start with.

You can choose one of the 16 different fillings:

Now we have more options:

$$6 \times 16 = 96$$

You can also choose to add any of the 8 vegetables:

This expands the number of options by a lot:

$$6 \times 16 \times 2^8 = 24576$$

Pick one of the 6 sauces available:

Now we have more options:

$$6 \times 16 \times 2^8 \times 6 = 147456$$

You also have some extra things to add on:

Now, the number of options equals:

$$6 \times 16 \times 2^8 \times 6 \times 2^5 = 4718592$$

As you can see, there are more than 4,718,592 possible combinations.