Final answer:
There are 32 different variations of nachos possible when Joe chooses from the given toppings.
Step-by-step explanation:
In this question, Joe can have nachos with just cheese or add any combination of chicken, onion, sour cream, and olives. To find the number of different variations of nachos, we can use the concept of combinations.
For each topping that Joe can choose to add or not add to his nachos, there are 2 options: either he adds the topping or he doesn't. So, for 5 toppings (including just cheese), Joe has 2 choices for each topping. Using the formula for the total number of combinations, which is 2^5, we find that there are 32 different variations of nachos possible.
Therefore, Joe can have 32 different variations of nachos at the Mexican restaurant.