Setting up negative binomial GLMM with multiple (8) predictor variables


I'm pretty new to R and I'm trying to create models using negative binomial GLMMs. The problem is, I have 1 response variable and I want to test 8 predictor variables for multicollinearity. It seems easy when, for example, there are only 3 predictor variables because that means only 4 possible combinations. However, I'm wondering if there is an easier way to set up all possible combinations for 8 different predictor variables when testing for multicollinearity without going through every combination by hand, which means some number far over 50 different combinations for 8 predictor variables to be tested against the response variable.

I've been using the "glm.nb" function in the MASS package and I'm unsure if there is a big difference between that and the "glmmTMB" package.