In the context of experiments, what does the notation (n1)(n2)...(nk) represent?

The notation (n1)(n2)...(nk) signifies the result of multiplying the number of options available at each individual step of a multi-step experiment. When conducting an experiment that consists of several steps, each step can have a different number of possible outcomes characterized by n1, n2, and so forth, up to nk. By multiplying these values together, you calculate the total number of unique combinations or outcomes that can arise from completing all steps in the experiment.

For example, if one step has three outcomes (n1 = 3) and another has four outcomes (n2 = 4), then the overall number of unique combinations from these steps is calculated as 3 * 4 = 12. This concept is pivotal in combinatorial problems, probability calculations, and structuring experiments where each choice can affect the outcome of subsequent decisions.

The other choices do not accurately reflect this notation. While they may relate to the broader context of probability and outcomes, option D directly addresses the mathematical operation represented by the notation in multi-step experiments.