Puzzle #201: Hotdogs

It is time to start your training for summer hotdog eating. Off you go to the local convenience store to work your way through the many combinations of toppings. LCS has the following toppings: mustard, relish, ketchup, chili, cheese, onion, garlic, and peppers.

If you can only have up to two of mustard, relish, and ketchup and at most one of onion, garlic, and peppers, how many different hotdog topping combos can you create?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, April 12, 2017 at noon Pacific Time. I will post the answer shortly after.