Hello,

I've been trying to figure out this simple problem but I'm just missing something.

Here it is:
I have 4 lights and at any given point half the lights will be on and the other half will be off. I have figured out that there are 6 different combinations where this is possible.

Ok, now move to 6 lights and the same is true, at any given point half the lights will be on and half will be off. I have figured out that there are 20 combinations possible.

With 8 lights there are 35 combinations possible.


Does anyone see a pattern or forumla I can apply?