At first try my answer is 6 but after checking it again and research (reference: google)
Looks like this is the answer you are looking for :
Case 1: The marbles are all the same color (G G G, B B B, R R R) - 3 cases
Case 2: Two marbles are the same color. (G G R, G G B, R R G, R R B, B B R, B B G) - 6 cases. It is important to note that this step also takes care of the case that there is one marble of a certain color and two of another. Such as (G R R), as this has been counted as (R R G) already.
Case 3: There is one marble of each color. (R G B) - 1 Case
3 + 6 + 1 gives us our answer, 10.