Final answer:
A tree diagram can be drawn to model the possible partnering of volunteers. The number of outcomes in the sample space can be calculated by multiplying the number of outcomes at each level of the tree. The probability of selecting Susan's name and the probability of selecting both Penny and Darren can be calculated using the number of outcomes and the total number of outcomes in the sample space.
Step-by-step explanation:
A tree diagram is a graphical representation that shows the different possible outcomes of an experiment. In this case, the experiment is the partnering of volunteers. To draw the tree diagram, start by labeling the overlapping section first, which represents the volunteers who can be both in a club and work part-time. Then, label the separate sections for volunteers who only belong to a club and volunteers who only work part-time. The number of outcomes in the sample space can be calculated by multiplying the number of outcomes at each level of the tree. The probability of selecting Susan's name can be found by dividing the number of outcomes where Susan's name is selected by the total number of outcomes in the sample space. The probability of selecting both Penny and Darren can be found by multiplying the probability of selecting Penny by the probability of selecting Darren, given that Penny has already been selected.