I'm having difficulty answering this question:

Suppose you are one of 42 people attending a conference. At every meal, the conferenceattendees are seated randomly at 7 tables, with 6 people at each table (so that you sit withfive other people at each meal). What is the probability that, at the next three meals, youwill sit with 15 different people?

We know that there are 6^7 ways of seating 6 people in 7 tables but then I don't know where to go from there.