21. From a faculty of six professors, six associate professors, ten assistant professors, and twelve instructors, a committee of size six is formed randomly. What is the probability that there is at least one person from each rank on the committee? Hint: Be careful, the answer is not ; 6 1 <;6 1 <;10 1 <;12 1 <;30 2 < ; 34 6 < = 1.397. To find the correct answer, use the inclusion-exclusion principle explained in Section 1.4.