Random Thoughts.....What Are You Thinking?

First, consider the eight base soft drinks on the menu (including cola, root beer and slush mix). If you make no assumption about how many add-ins are used, then there are two possibilities for each of the 16 add-ins: Either you use it or you don’t. Multiply the two possibilities 16 times, and you get 65,536 possible combinations of add-ins for each base drink. Multiply that by eight, subtract one — because no one orders flavorless slush mix by itself — and you get 524,287. Then there are five more base drinks that are made up of one of the add-ins, plus water (such as Powerade). Each of these have one fewer add-in possibility, as you wouldn’t add Powerade to Powerade. Multiply 5 by 2^15 and you get 163,840. Add them up, plus six other beverages that don’t come with add-ins (such as coffee and orange juice) and you arrive at 688,133.