If I have 7 different attributes 1, 2, 3, 4, 5, 6, 7 that need to be combined into as many unique groups of 4 as possible, but 6 and 1, 6 and 3, and 3 and 4 are incompatible with each other what should I do? No repeats and order doesn't matter.
(K = 4, N = 7) ${}^{7}C_{4}$
Incompatibilities: (6 and 1), (6 and 3), (3 and 4)
I know I can reverse engineer it by making 1 of my incompatible groups required instead of incompatible (K = 4-2, N = 7-2) = (K = 2, N = 5) ${}^{5}C_{2}$ then finding the difference between my full answer and incompatibles answer ${}^{7}C_{4}$ - ${}^{5}C_{2}$, but I don't know what to do if there are multiple incompatibilities.
I've mapped it out if anyone cares to analyse...