Let me show what I have tried so far...

By the way, I am not a student (although I wish I were!) - I am 62 and trying to find ways to creatively spend my free time

Starting by the rows, I've written down all possible combinations of A, B and C which are 45 in total (9+8+7+...+1). Of those, we keep only the arrangements that meet the required restrictions, i.e. A>=B and A>=C (I mean, number of As, Bs and Cs).

These are the following 17:

3 2 3

3 3 2

4 0 4

4 1 3

4 2 2

4 3 1

4 4 0

5 0 3

5 1 2

5 2 1

5 3 0

6 0 2

6 1 1

6 2 0

7 0 1

7 1 0

8 0 0

We then do the same with the columns, where we keep only the 13 arrangements.

0 4 3

0 5 2

0 6 1

0 7 0

1 3 3

1 4 2

1 5 1

1 6 0

2 3 2

2 4 1

2 5 0

3 3 1

3 4 0

I don't know what to do next. We can see, for example, that in the rows, we have a minimum of 0 and maximum 4 Cs - but we can't simply say that the total minimum / maximum for the entire board is 0 and 4*7=28, right? Same also with the columns (0 - 3*8=24).