How can I have multiple combination restrictions? 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.
 A: I've mapped it out if anyone cares to analyse...

1234 (34)
1235
1236 (16)(36)
1237
1245

1246 (16)
1247
1256 (16)
1257
1267 (16)

1345 (34)
1346 (16)(34)(36)
1347 (34)
1356 (16)(36)
1357

1367 (16)(36)
1456 (16)
1457
1467 (16)
1567 (16)

2345 (34)
2346 (34)(36)
2347 (34)
2356 (36)
2357

2367 (36)
2456
2457
2467
2567

3456 (34)(36)
3457 (34)
3467 (34)(36)
3567 (36)
4567

A: I don't have an equation, but there's an easy way to do it manually.
Start with the numbers in order 1234. Then you can change the last number to the next number up one 1235, do this until you've done this with the rest of the numbers 1236 1237. Then change the second to last character to the next highest and repeat the last step. 1245 1246 1247. Then you can continue moving down the line 1256 1257, 1345 1346 1347 1356... While making it or when you're done you can dismiss the incompatible ones. It feels like it shouldn't work, but I don't know.
Maybe there's something here for an equation, but I'm not smart enough to make one.
