I have 2^k possible vectors (eg: 2^4 = 16) of length k.
I want to select n (where k < n+1) vectors (eg: n = 7). k vectors must form a linearly independent set AND the other (n-k) vectors must also be linearly independent when viewed seperately.
I do not want all the solutions. I simply want to determine what the probability is of finding such a selection in the first 7 packets I choose.