I’m determining some “straightforward” math calculation for my thesis. That is one thing I’ve discovered someplace in highschool however I can not fairly keep in mind the way it’s achieved. Possibly you guys will help me with this downside….

So I’ve eight entities, shall we say $A_1, A_2, …, A_7, A_8$. All of the entities can both maintain one of many three values -1, Zero or +1. Assume that there ought to all the time be at two $A_i$ that maintain a worth of -1 or +1, thus there can by no means be extra that six $A_i$ that maintain a worth of 0. What number of combos are there. Be aware that in each mixture of $n$ variety of combos each $A_i$ can be utilized as soon as. For instance:

OK:

$A_1=+1$, $A_2=+1$, $A_3=+1$, $A_4=+1$, $A_5=+1$, $A_6=+1$, $A_7=+1$, $A_8=+1$

$A_1= 0 $, $A_2=+1$, $A_3=+1$, $A_4=0$, $A_5=+1$, $A_6=+1$, $A_7=+1$, $A_8=+1$

NOT OK:

$A_1=0 $, $A_2=0$, $A_3=0$, $A_4=0$, $A_5=0$, $A_6=0$, $A_7=0$, $A_8=1$

or

$A_1=1 $, $A_1=0$, $A_1=1$, $A_4=0$

This needs to be frequent knwoledge to me, however I can appear to determine it out. Your assist is way appreciated.

Yours,