Recent curricular developments suggest that students at all levels need to be statistically literate and able to efficiently and accurately make probabilistic decisions. Furthermore, statistical literacy is a requirement to being a well-informed citizen of society. Research also recognizes that the ability to reason probabilistically is supported and enabled by other forms of mathematical reasoning and concepts. One of these supporting concepts is sample space, the enumeration of all outcomes of a probability experiment. As a concept, sample space supports the construction of probability distributions, which in turn enables statistical inference, a form of probabilistic reasoning. This mixed methods study investigated how undergraduate pre-service elementary teachers construct and generalize their understanding about sample space. One hundred fifty students participated in a series of three tasks designed to investigate the ways in which they enumerate sample space and the associations between their enumeration strategies and their generalization rules. A subset of eight participants engaged in follow-up interviews designed to explore their understandings of sample space enumeration and generalization. Findings from the study suggest that there was growth across tasks in the sophistication of the enumeration strategies used and that participants attempted to find explicit and formalized generalizations. However, in spite of this growth in the sophistication of enumeration, there was little association between the enumeration strategies participants used and the generalizations that they constructed. Students compartmentalized their understanding of generalization rules, often looking for a numeric formula that had little do to with their enumerated solutions. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]