I'm not sure if this is what you're looking for, but in terms of q-factorials you could write this as .
Off topic, but does this gives the permutation of sequences with r linearly independent vectors in a dimension n vector space over ? Unless, the formula I solved for was incorrect, I think this should involve combinations?
I'm not sure if this is what you're looking for, but in terms of q-factorials you could write this as .