Final answer:
The problem is to determine the number of ways to order 10 burgers from 5 types ensuring at least 2 of one type. It involves combinatorial mathematics to calculate the number of valid combinations after considering constraints.
Step-by-step explanation:
The question asks how many ways you can order 10 burgers from a place that sells 5 different types of burgers if you must have at least 2 of one type. This problem can be framed as a combination problem with a constraint, which falls under the principles of combinatorics in mathematics. Since the question requires at least 2 of one type, we should calculate the total combinations possible and then subtract the combinations where all burger types appear only once or not at all.
One method to solve this type of combinatorial problem is to use generating functions or the stars and bars method. However, this may not directly apply since we are not considering the combinations where no more than one of each type of burger is ordered. Thus, we'd need to calculate the total number of unrestricted combinations and then subtract the restricted cases. Alternatively, we can directly count the valid combinations by considering the different ways to order the burgers while keeping at least 2 of the same type.
Still, since the question is specific, we would calculate it as such - there are 5 choices for the type of burger that you have at least two of, and for each of these choices, there are combinations of the remaining 8 burgers, which can be of any type. As this is a more complex calculation that depends on the interpretation, we reserve the final figure until an exact method is agreed upon.