Prior works have shown that in-context learning is brittle to presentation factors such as the order, number, and choice of selected examples. However, ablation-based guidance on selecting the number of examples may ignore the interplay between different presentation factors. In this work we develop a Monte Carlo sampling-based method to study the impact of number of examples while explicitly accounting for effects from order and selected examples. We find that previous guidance on how many in-context examples to select does not always generalize across different sets of selected examples and orderings, and whether one-shot settings outperform zero-shot settings is highly dependent on the selected example. Additionally, inspired by data valuation, we apply our sampling method to in-context example selection to select examples that perform well across different orderings. We find a negative result, that while performance is robust to ordering and number of examples, there is an unexpected performance degradation compared to random sampling.