# Lay's Do Us a Flavor Contest

**2/6/16**

Over the last few years, Frito Lay (ie. Pepsi) ran a "Do Us a Flavor" contest, where the public would submit their ideas for new potato chip flavors, with the winner winning some serious cash, or you could say "all the chips" (couldn't resist). I thought of all the possible ingredients and combinations of ingredients, and knew this would be an interesting application of probability and statistics.

Say you have a list of N ingredients to choose from, and they can be submitted in 1, 2, or 3 ingredient submissions. For example, your ingredients are apple, lemon, and salmon. Then some possible submissions are: lemon, apple, apple and lemon, salmon, apple and lemon and salmon, etc. The question is, what is the total number of possible submissions, S, you can submit? It turns out that

where nCr(n,r) is the number of combinations of n things chosen r and a time. These numbers get very large and very fast. Note that the "3*" is there because in the contest you could also submit a "chip style" of kettle, original, or wavy. Obviously not all of these submissions are guaranteed to be tasty. In fact, the majority will probably be quite odd, so S effectively is a lot smaller.

I controlled if the submission has 1, 2, or 3 ingredients in it also by using probability. I set Prob(3 ingredients) = 10%, and P(2 ingredients) = 80%.

By using combinations instead of permutations I took into account that, for example, lemon and apple is the same ingredients as apple and lemon. In the spreadsheet I also checked if one submission was the same as a previous submission to help eliminate duplicate submissions.

My spreadsheet for 2014 had 617 ingredients. This gives S = 117,444,099 as the total number of possible submissions. I ended up submitting about 26 I thought were pretty good. I didn't win, but it sure was fun!

I enjoyed generating and submitting ideas for the Do Us a Flavor contests over the last few years. The sheer number of possibilities made me consider ingredient combinations I never could have imagined if it wasn't for a systematic approach using randomness.

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