I'm fairly sure that I have to use a binomial distribution for this question but would love some help in setting it up and a description on how to solve it:

A small high school has 20 teachers. All of the teachers eat their lunch at one of two diners, and they are just as likely to eat in one as in the other. If the owners of these diners each want to be at least 90% sure that there will be enough seats to accommodate the teachers, how many seats must each of the diners have? Justify your