Tiantian goes to the cafeteria for lunch. She needs to choose a set meal consisting of one meat dish, one vegetable dish, and one drink. There are three meat dishes: Kung Pao Chicken, Cumin Lamb, and Sweet and Sour Pork. There are three vegetable dishes: Braised Eggplant, Di San Xian, and Stir-fried Loofah. And there are three drinks: Milk, Orange Juice, and Water. How many different combinations can she make?
To solve this problem, we use the multiplication principle. When we need to make multiple independent choices, we multiply the number of options for each choice. In this case, Tiantian has 3 choices for meat dishes, 3 choices for vegetable dishes, and 3 choices for drinks. So the total number of different set meals is 3 times 3 times 3, which equals 27.
We can also visualize this problem using a tree diagram. Starting from the root, we have 3 branches for meat dishes. From each meat choice, we have 3 more branches for vegetable dishes. And from each vegetable choice, we have 3 final branches for drinks. Each complete path from root to leaf represents one possible set meal. Counting all the paths, we get 27 different combinations.
Let's break down the calculation step by step. In step one, Tiantian chooses a meat dish from 3 options. In step two, for each meat choice, she has 3 vegetable options. In step three, for each meat and vegetable combination, she has 3 drink options. So we multiply 3 times 3 times 3, which gives us 27 different set meals that Tiantian can choose from.