Final answer:
Customers at a car dealership can choose from 1,024 possible upgrade combinations, calculated using the formula for the number of combinations where each of the 10 upgrades can either be selected or not.
Step-by-step explanation:
The question asks for the number of possible combinations when selecting upgrades from a set of 10 offered by a car dealership. This is a typical problem of combinatorics, which is a branch of mathematics that deals with counting combinations and permutations of a set of elements. Each upgrade can either be selected or not, which gives us two choices (select or don't select) for each upgrade. Therefore, we can use the formula for the number of combinations of n items taken k at a time, which is n choose k. In this case, because any number of upgrades can be chosen, we sum the combinations for all possible values of k from 0 to 10. This is equivalent to calculating 2 to the power of the number of items (2^10) because we have two choices for each of the 10 upgrades. Therefore, there are 2^10 or 1,024 different potential upgrade combinations a customer can choose from.