Need help finding a Function to this type of question (probability and statistics related)?

Question

Say I have eight charges. I want a function that would determine that maximum number of possible charge-charge interactions. Is there something like this?

Answer 1

Consider the interaction between two charges, x₁ and x₂

You have 8 choices for x₁, and then since you chose one already, only 7 choices for x₂. That would be a total of 8 × 7 = 56 interactions.

But, if you consider that the interaction of x₁ with x₂ is the same as the interaction of x₂ with x₁, then you've really only got half as many, or 56/2 = 28 interactions.