6 ppl sit around one roundtable. number of comb is 5!.
when 2 ppl must sit together. take the 2 ppl as one unity. so its 4! comb. but the 2 ppl can change seats within the unity. its 4!*2.
when 2 ppl must not sit together. total com - 2 ppl must sit together. 5! - 4!*2.
If your mind can conceive it and your heart can believe it, have faith that you can achieve it.