Final answer:
The correct number of different variations of pasta with tomato sauce using the given ingredients is 16, considering each ingredient can be either included or not.
Step-by-step explanation:
When calculating the number of different variations available for ordering pasta with tomato sauce using the ingredients { onions, garlic, broccoli, mushrooms }, it is important to recognize that we are dealing with a combination problem. Each ingredient can either be included or not included in the tomato sauce, which means we have two choices for each of the four ingredients. This gives us 2 to the power of 4, or 16 possible combinations. Thus, the correct answer from the listed options would be 16 variations; however, it's important to note that the second part of each option (e.g., '4 ways', '16 ways') does not make sense in this context as the number of variations is 16 from the given set.