Let's start with a simple one!

After giving one mark to each question, $7$ marks are to be distributed among $3$ questions.So, the required number of ways are given by the number of non-negative integral solutions of $x+y+z=7$ where $x,y$ and $z$ are the $3$ questions.

If first question receives 1 mark, solutions are: 1,1,8 1,2,7 1,3,6 ... 1,8,1 --> 8 solutions If first question receives 2 marks, solutions are: 2,1,7 2,2,6 2,3,5 ... 2,7,1 --> 7 solutions ... If first receives 8 markts, solution is: 8,1,1 --> 1 solution

8+7+6+5+4+3+2+1 = 36

I just used stars and bars (see https://brilliant.org/wiki/integer-equations-star-and-bars/) where there are 2 bars and 9 gaps so there are 9C2 = 36 combinations.