Nine people sit down at random seats around a round table. Four of them are math majors, three others are physics majors, and the two remaining people are biology majors. What is the probability that all four math majors sit in consecutive seats?
There are a total of $(9-1)!=8!$ possible seating arrangements. We treat the four math majors as a single person. So we're really seating 6 people around a table which gives $5!$. So the probability is $5!/8!$. I think this is wrong. Any help is greatly appreciated.