A student must pick 5 classes from 12 courses, if he must have at least one WH class or USH class, how many different choices does he have? The World History course and United States history course is already part of the 12 courses he must choose from. It is required to have at least one of these classes in his new class schedule. Sorry if my question didn't make sense earlier, this question was from a practice exam I'm just recalling the question from memory. I was short on time so I just solved C(12,5) and I know its wrong because I forgot about the at least. This has been bugging me all day and I'd appreciate it if someone can explain. 

We will take "At least one USH or WH" to mean that you could take all five courses from this set. This is odd, but it is the best semantic match for the question wording. If it is supposed to mean one or both, this approach wont work.
In this case, the  "stars and bars"  technique applies. Ken Ribet is a better teacher than I. If you don't have time for a sixteen minute video, here's a summary:
Your question can be reframed by asking how many ways can you toss k balls into n buckets. Or, how many ways can you insert n - 1 separators into a list of k potential courses. The spaces in between separators represent different buckets (potential courses). There are one fewer separators than buckets because extremal areas count as buckets so the formula is:  
${n+k-1\choose k}$
Your question is further complicated by the initial condition of at least one course of two potential types. Now we can count the possibilities by separating into ways of choosing courses from the first two types:
1 History: ${1+2-1\choose1} * {4+10-1\choose4}$ +  
2 History: ${2+2-1\choose2} * {3+10-1\choose3}$ +  
3 History: ${3+2-1\choose3} * {2+10-1\choose2}$ +  
4 History: ${4+2-1\choose4} * {1+10-1\choose1}$ +  
5 History: ${5+2-1\choose5}$
