Question

A waffle house offers 19 different types of syrups. If a customer can choose any number of syrups to have with their waffle, how many syrup combinations are possible? Please show work

Answer 1

The total number of syrup combinations is 524,288.

Step-by-step explanation:

To find the number of syrup combinations, we can use the concept of permutations. Each syrup has two choices: either it is chosen or not chosen. Since each syrup can be chosen or not chosen independently, there are 2 choices for each syrup. Therefore, the total number of syrup combinations is 2^19.

Using the exponential rule, we can calculate 2^19 as:
2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 524,288.