since the order of the selected puppies is not important we need to find the number of all the different subsets of 3 elements of the set of 12 breeds of puppies:

C(12, 3) = 12!/(3!(12-3)!)

C(12, 3) = 12!/(3!9!)

C(12, 3) = 10*11*12/6

C(12, 3) = 220

there are 220 varieties.