Calvin's Cream Conundrum

Calvin is at an ice cream store, which offers 12 flavors of ice cream. A 3-in-a-cup consists of 3 scoops of ice cream, placed in a cup. The order of placement of the scoops of ice cream doesn’t matter. The shop has a banner proclaiming "Choose from 1000++ different combinations of 3-in-a-cup!”, but Calvin says that is not true. How many different combinations of 3-in-a-cup are there?

Details and assumptions

A cup consisting of 2 scoops of chocolate and 1 scoop of vanilla is considered different from a cup consisting of 1 scoop of chocolate and 2 scoops of vanilla. However, the former is equivalent to 1 scoop of chocolate, added to 1 scoop of vanilla, added to 1 scoop of chocolate.

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