N(A OR B) = N(A) + N(B) - N(A AND B)

6 male professors, 11 female professors, 10 male teaching assistants 
and 12 female teaching assistants

N(professors) = 6+11 = 17
N(males) = 6+10 = 16
N(professor and male) = 6

N(professor OR male) = N(professors) + N(males) - N(professor AND male)
N(professor OR male) = 17 + 16 - 6 = 27

N(people to choose from) = 6+11+10+12 = 39

The probability is 27 out of 39 = 27/39 which reduces to 9/13

Edwin