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?

TheMathCoder  Apr 26, 2018

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%



cool cool cool

CPhill  Apr 26, 2018

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