The multiplication principle serves as a cornerstone in enumerative combinatorics. The principle underpins many basic counting formulas and provides students with a critical element of combinatorial justification. Given its importance, the way in which it is presented in textbooks is surprisingly varied. In this paper, we analyze a number of university textbooks in order to explore and identify several key aspects of the various statements of the principle. We characterize the nature of the variety of statements by identifying structural, operational, and bridge statements, and we highlight the respective statements' mathematical and pedagogical implications. We conclude by indicating several directions for future research.