Can I replace "a range of" with "a variety of"? If not possible, could you explain why?
Yes, I would say that either "range of" or "variety of" would be fine in this example. Please note that the word "range" lightly implies some sort of continuation, meaning that the things being considered could be put into some kind of order or sequence. You could have a range of prices, or a range of colors. It can be used on things where this is less natural and obvious, like food types, but might not be the best choice. The word "variety", on the other hand, is just a bunch of different things. There doesn't need to be any kind of ordering. If there is an obvious ordering, like with prices, it would probably be better to use "range". Ex: The restaurant offers a variety of food. Ex: The store sells a variety of furniture. Ex: The dog exhibits a range of behavior. Ex: I offered him a range of options.
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