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.