To determine which statements are correct, let's analyze the problem:
Sara can choose between two types of countertops (granite or quartz) and three colors (charcoal, white, or sand).
A - {GC, GW, GS, QC, QW, QS} is the sample space.
This statement is correct. The sample space represents all possible combinations of countertop type (G or Q) and color (C, W, or S).
B - Sara can choose from 5 combinations.
This statement is incorrect. Since Sara has two options for countertop type and three options for color, she has a total of 2 x 3 = 6 combinations to choose from.
C - Sara can choose from 6 combinations.
This statement is correct. As explained above, there are 6 possible combinations for Sara to choose from.
D - {G, Q, C, W, S} is the sample space.
This statement is incorrect. {G, Q, C, W, S} represents the set of individual options available (countertop type and colors), but not all the combinations.
E - {GQ, C, W, S} is the sample space.
This statement is incorrect. {GQ, C, W, S} represents a mix of countertop type and colors, but it does not cover all the possible combinations.
So, the correct statements are A and C.