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?
If we "anchor" any one person in a seat, there are 8! arrangements of the other peoeple that are possible = 40320 arrangements
If we "anchor" the mathematicians in any 4 consecutive positions there are 4! = 24 arrangements of them that are possible
And the other people can be arranged in 5! = 120 ways
So....the total number of ways that the mathematicians can be seated is 24 * 120 = 2880 ways
So....the probability that all 4 math majors sit in consecutive seats is 2880 / 40320 = 1/14 ≈ 7.14%