# proving a certain split is impossible

I am struggling with a question that involves splitting 50 people into a max of 6 groups and then splitting the same 50 people into a max of 8 groups, while having completely different groups in the second split; i.e., if $a,b$ were together in the first split they can't be together in the second split.

I need to prove that this is an impossible requirement to fulfill. I know it has to do with having more pairs then possibilities but I can't seem to manage to prove this.

If $50$ people are split into $8$ groups, how many members must the largest group at least have? Can the members of that largest group all have been in different groups in the first split?