Jane and tim are struggling to decide which restaurant to go to for dinner. they have 10 options to choose from, and they each have an order of preference for these restaurants which is hidden from the other person. furthermore, their preference orders are independent of each other. in order to decide where to go as fairly as possible, they agree that jane will pick 5 options to remove from the list, after which tim can choose where they will eat from the remaining 5 options. the probability that the restaurant tim decides upon is not in the top 3 of either person's preferences can be expressed in the form
m/n
, where
m
and
n
are relatively prime positive integers (i.e. their greatest common divisor is 1 ). compute
m+n