I started by doing Level 2 as 123, 124, 125, 126, then 134, 135, 136, because anything with 2 in it would repeat, then 145, 146, finally 156 which is 10 cominations all containing particle 1 on Level 1.
Now I needed to do the combinations that didn't have particle 1 in them.
Start 234, 235, 236, then 245, 246, then 256. Next 345, 346, 356 Finally 456. That gives a grand total of 20. I've instinctively missed out many combinations as being repeats of earlier ones (number order doesn't matter here) but I hope I've not been careless.
