The multiplication principle (MP) is a fundamental aspect of combinatorial enumeration. In an effort to better understand students' reasoning about the MP, we had two undergraduate students reinvent a statement of the MP in a teaching experiment. In this paper, we adopt an actor-oriented perspective (Lobato, "Educational Researcher," 32(1), 17-20, 2003, "Educational Psychologist," 47(3), 1-16 2012) and draw on Lockwood's, "Journal of Mathematical Behavior," 32, 251-265 (2013) model of students' combinatorial thinking to trace the students' development of a certain conception about order -- that a statement of the MP should allow for any ordering of the stages of a counting process. Notably, this conception differs from how order is treated in textbook statements of the MP. We report on how this conception persisted for the students, and we explain how the researchers (interviewers) and students managed to proceed through the teaching experiment while maintaining different conceptions of order. The students' reasoning about order sheds light on ways in which students may think about order and highlights potential subtleties about multiplication in counting that deserve attention.