I submitted this problem, but it was rejected since it does not fit well into any of the categories [EDIT: or not] (I personally thought it could fit into Combinatorics, what do you think?).
There are 15 marbles in a bag, in exactly 5 different colors. Grabbing marbles randomly without replacement, it takes at most 9 grabs to get three marbles of the same color, and at most 14 grabs to get five marbles of the same color.
Find the sum of the maximum number of grabs it takes to get four of a color in each of the possible arrangements that satisfy the above conditions.