No problem, let me provide a complete explanation to help you understand the problem.
Sara is trying to decide on the type and color of the new countertops for her kitchen. She has two choices: granite (G) or quartz (Q). She also has three color choices: charcoal (C), white (W), or sand (S).
To determine all the possible combinations, we can create a sample space:
{GC, GW, GS, QC, QW, QS}
This represents all of the possible combinations of type (G or Q) and color (C, W, or S). Therefore, statement A, "{GC, GW, GS, QC, QW, QS} is the sample space," is true.
However, statement D, "{GQ, C, W, S} is the sample space," is not true. This is because GQ is not a possible combination for the countertops - Sara can only choose one type of countertop, either G or Q. The correct sample space includes the possible combinations of type and color, which leads us back to statement A.
To determine how many combinations Sara can choose from, we can count the number of outcomes in the sample space. There are six possible outcomes, so statement E, "Sara can choose from 6 combinations," is true.
Finally, statement C, "Sara can choose from 5 combinations," is not true. This statement implies that there are 5 distinct combinations to choose from, but as we saw in the sample space, there are 6 possible outcomes. Therefore, statement C is false.
In summary, the correct statements are A and E.