Suppose that an ice-cream café has 10 different flavors of ice cream. In how many different ways one can choose 3 scoops of ice-cream, so that order of flavors does not matter?

If the order does not matter, use combinations. It the order does matter, use permutations.
So in this case, You have to add the possibility that all three scoops are of different flavors, two scoops are from the same flavor, and all three scoops are of the same flavor:$$\binom{10}{3}+2\binom{10}{2}+\binom{10}{1}$$