The Waffle House is bad at combinatorics.
Last time I visited the Waffle House in Atlanta, I took a photo of their menu. This section of the menu shows the various ways that they can prepare your hashbrowns. Notice that there are three sizes (regular, large, and triple) and seven options (smothered, covered, chunked, topped, diced, peppered, and capped). That means that the number of possible ways of ordering your hashbrowns is
3 * 27 = 384.
However, as you can see in the photo, they claim that there are 1,572,864, or 3 * 219 ways to prepare your hashbrowns. Where does this number come from? Are there “secret” hashbrown options that aren’t on the menu?
||Jessica Simpson is also bad at combinatorics.
Now, let’s carefully consider the total number of options. Each of the four pizzas is allowed up to four toppings, and there are a total of 18 toppings to choose from. Assuming no repeated toppings, there are 18 choose 4, or 3060, possibilities for each individual pizza. Since there are four pizzas, the total number of overall options on the 4forAll is 3060 choose 4, or approximately 3.6 trillion. This is assuming that no two pizzas are identical and that no pizzas have repeated toppings (e.g. extra cheese, double pepperoni). If we discard these two assumptions the number of possible combinations is even greater! So although Jessica was technically correct when she stated that there were “more than six million topping options,” this is a pretty crappy estimate — it’s off by six orders of magnitude. This is particularly embarrassing given that the commercial’s main “joke” was Jessica’s “ironic mathematic acumen.”
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