Q:

Wide variety or wide choice (in context)

Fill in the Blanks
We offer a wide ....... of classes in this school. 

case
variety
part
choice

For me a wide variety of classes imply that we have various classes (in different subjects) and wide choice of classes imply that you have a lot of classes to choose from (and attend in).  But the questions of the book in which I found this question have one valid answer and I don't know which one is right and I am not native so I cannot be sure about the feeling I get from each answer. 
So, which answer is right (or more appropriate)? 

A:

From a strictly technical standpoint, both 2.  and 4.  are grammatically correct.  An answer depends on the intention of the question. 

You could have 20 courses that cover 5 subjects in total: this shows a wide choice of classes. 
You could have 10 courses that cover 10 subjects in total: this shows a wide variety of classes. 

But, having said that, I find a wide choice to be awkward because I'm not used to hearing it—I'm not even sure I'e ever heard it. ( I'm used to a wide selection instead.) 
If the word is choice, I think that large choice is more common. ( Which is not an available option.) 
In contrast, I've heard both wide variety and large variety.  Don't ask me why; English is annoyingly illogical. 
In conclusion, I would choose 2.  because it is both grammatically correct and more common.