From a faculty of 6 full professors 6 associate professors 1

From a faculty of 6 full professors, 6 associate professors, 10 assistant professors, and 12 lecturers, a committee of six is randomly formed. What is the probability that there is at least one person from each rank on the committee (You will need to use inclusion/exclusion to do this problem)

Solution

pick one from full profs = 1/6

pick one from associate prof = 1/6

one from assistant prof = 1/10

one from lecturer = 1/12

other remaining 2 people can be picked form remaing people 2/ (5+5+9+11) =1/15

so probability = 1/6*1/6*1/10*1/12*1/15 = 1/3240 -----------answer