Using both physical and Fathom™ virtual coins Year 10 students explored the distinction between coin-sequences and coin-combinations (where the order is not important) presented as companion tasks within an integrated coin system. This approach sought to highlight two key concepts within the one teaching unit: coin-sequences, to examine independent events, and coin-combinations, to examine the binomial distribution. The misconception that a particular coin-sequence (e.g. HHHHH) is less likely to occur may arise when a coin-sequence task is re-interpreted incorrectly as a coin-combination (e.g. 5 Heads). Pedagogy was based on principles that emphasised profound understanding through the use of multiple approaches to problem solving.