Question 1: A committee is to be formed from the History and Geography departments at UCT. The 9 people on the committee can be selected from 15 eligible individuals located in the two departments: 7 of these are in the History department (including the HOD), and 8 are in the Geography department (including the HOD). a) bl 1') 3) With no regard to which departments the members come from, or restrictions on how many come from which department, how many different committees of size 9 could one construct out of the 15 eligible people? How many ways could any particular committee line up for a photograph (how many different photos with different arrangement of members for a given committee). If it is required that all 7 potential History department members have to be on the committee, how many different committees could be formed. For any particular committee formed in c) above, how many photos could we construct if the Geography members insist on sitting together. For any particular committee formed in c) above, how many photos could we construct if the History members insist on sitting in a single contiguous group (no Geography members in between)? For any particular committee formed in e) above, how many photos could we construct if the HOD of History insists on sitting in the middle. If the specific request of the HOD of History was ignored, what is the probability that a randomly configured photo with the restrictions of e) happens to end up WITH the HOD of History seated in the middle