The Rosada family has had tremendous success selling tostadas at their restaurant and now they want to expand their menu. They want to feature combination plates with a choice from six Mexican dishes: quesadillas, enchiladas, burritos, tamales, tacos and chiles rellenos. They want their customers to be able to choose three different items on their combination plates. The Rosada family wants to know how many combination are possible. Juanita, who is one of their four children, came up with the answer of 18 different combination plates. She used a grid just like you had used. Do you agree or disagree with Juanita's answer?
To answer this question, Quentin made a flip-book. Each third has all six dishes, so he could use them to make all the possible combinations. All he had to do was make sure that he didn't repeat any dishes, because all combinations must have only one serving of each dish. He wrote down the combinations, using abbreviations for each of the dishes, such as Q-T-B for Quesadilla-Tamale-Burrito. He disagreed with Juanita's solution. Do you?