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When you are dealing with a set of options to determine the total number of possiblities you have to take the base set and put it to the factor of the number of variables. For example, license plates, if you go with the standard three letters and three numbers then you have the possibility of 17,576,000 (26^3*10^3), of course this doesn't count for the entire series that they throw out such as ASS, KOK, FUK, and etc, but the basic principle still applies.
When you have a set with combinations, lets say for instance a pizza, where you can have multiple versions of the same choices then your variations are based on 2 to the factor of the number of possibilities. To go with the pizza example lets say you have ten different toppings to choose from, you would then have 1024 (2^10) different types of pizza you could order. I'll break this down in a simpler example so you can see the math. Your toppings choices are Pepperoni, Sausage and Ham, that would give us 8 (2^3) as the number of pizzas you could order:
As you can see, you have the eight aforementioned different types of pizza.
At this point you, or really probably somewhere in the first paragraph, you may be asking yourself "But Pete, why does this have any meaning?" Well let me tell you. I like to get a particular breakfast sandwich in the morning; sausage patties, scrambled eggs (in a flat sandwich type form) and a slice of American cheese on a bagel. This really should result in a single type, but yet I have received so many variations of this sandwich it staggers my mind:
So my simple 2^1 breakfast becomes a possible 64 (2^6) variant fiasco. It shouldn't be this way, and yet it is a place I find myself in all too often. So when I get a disappointement in the breakfast department, I find myself turning to the math behind it to see if somewhere I can make some sense of the whole deal.
I suppose its arguable if the proceeding example does make any of the sense I am seeking, but from my standpoint, at least its fun to crunch the numbers.
