1. The problem statement, all variables and given/known data An experiment has 3 outcomes. If the experiment is performed 4 times, how many sets of outcomes exist in which exactly two of the experiments had the same outcome. 3. The attempt at a solution From what I understand there is a 4-element set with each element having 3 possible values. So there are 34 = 81 such sets. The question is asking how many sets contain elements where exactly two of the elements are equal. I'm having trouble understanding how to count these. I imagine starting with 4C2 to get the number of ways to get two of the elements to fit a specific criteria, but I don't know how to continue. Is there a general formula or reasoning process I am missing here?