Some hints that you should probably think hard about:
The first skill you need to develop is guessing what function to look up in the Mathematica help system. Your problem description includes "how many ways can you mark" and that might make you think of the word "Permutations". Can you find that in the help system and see how that might help you with this problem?
That can give you fifteen items, or lots of lists of fifteen items and you probably want to have each of those divided up into groups of three. You might or might not know the word "Partition". Perhaps you can think how that will help you with this problem.
Less likely that you would be able to guess the next word, but "Map" is something that you should definitely learn how to use. In the help system the examples may include lots of # and & and even /@ and those may be more confusing than helpful at this stage. You can figure those out later. For now you can figure out how to define some function like f[x_]:=2*x; and then Map[f, {1,2,4,z}] and see how Map is "going to do f to every item in that list". When you have practiced a bit with Map then you might start thinking how Map might be used to help you with this problem. You are likely to need to use Map more than once to solve this problem.
You might also use functions like Total and Length and perhaps DeleteCases, but there are always a dozen different ways of doing anything in Mathematica and you may use other functions instead.
If you study this carefully and search the help system and try to imagine how these pieces could be used to get closer to your answer then you should find that your skills have improved and the next problem you need to solve will be easier.
I urge you to not let someone just show you the answer. That won't help you nearly as much with your next problem.
Please let us know how much progress you have made.
