Please don't post so many questions at once!
Please also fix your latex.
However I know the questions you are asking :)
for the marvin one, 12c5 to get to 5,7 and 7c3 * 5c1 passing throguh 4,3
Now you calculate.
4 choices for each ball, 4 boxes, you can solve now.
these are the groups
4-0-0-0, 3-1-0-0, 2-2-0-0, 2-1-1-0, and 1-1-1-1
The number is answer.
C)
I answered this a few minutes ago.
Go see my answer earlier.