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.
Cans anyone please help?
Thanks.