# 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

S = 3*(nCr(N,1)+nCr(N,2)+nCr(N,3))

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.