SOLUTION
From this question, we can see that the Provost randomly selected 3 members from each department, which means the entire people in the faculty were grouped in a homogenous group which is "the departments" and 3 were then randomly selected from each homogenous group. Such type of sampling in which an entire population is divided into homogeneous groups and random samples are then taken from each group is know as Stratified random sampling.
Hence, the 4th option (Stratified sampling) is the correct answer.