The chancellor of a state university is applying for a new position. At a certain point in his application process, he is being considered by seven universities. At three of the seven he is a finalist, which means that (at each of the three universities) he is in the final group of three applicants, one of which will be chosen for the position.
At two of the seven universities he is a semifinalist, that is, one of six candidates (in each of the two universities). In two universities he is at an early stage of his application and believes there is a pool of about 20 candidates for each of the two positions.
Assuming that there is no exchange of information, or influence, across universities as to their hiring decisions, and that the chancellor is as likely to be chosen as any other applicant, what is the chancellor's probability of getting at least one job offer?