Question

A waffle house offers 22 different types of syrups. If customers can choose any number of syrups to have with their waffle, how many syrup combinations are possible? Leave your answer in exponential form.

Answer 1

For each kind of syrup, there are two options: to use it or not to use it.

To find the total amount of syrup combinations that are possible, we should multiply the number of options for each choice.

In this case, there are 2 options for each of the 22 choices. Then, the number of combinations possible, is equal to:

`2*2*2*\ldots*2\text{ (22 times)}`

Which is equal to:

`2^(22)`

Therefore, the answer is:

`2^(22)`