If a hot dog vendor offers 18 different condiments; how many condiment combinations are there?

Answer 1

If the vendor offers no condiment, there is only one choice: nothing!

If he offers one, then there are two choices, i.e. to "@nothing", the customer can add "nothing", or add the new condiment, that makes two choices.

If the vendor offers two condiments, then to each of the previous choices, the customer can choose to take it, or leave it. So this doubles the two choices to four.

This goes on doubling for every additional condiment the vendor adds, so the total number of combinations is
2^n=2^18, including any number of condiments up to and including 18.