Is there an analytic way to solve expected hamming distance of two randomly sampled binary (zero or one) strings of length n, where there can only be
k ones and
n-k zeros (aka n choose k)?
For example, given a 5 digit string 01101 which matches the above requirement of (n-k)=2 zeros, (k)=3 ones, what is the average hamming distance of this string and all other samples drawn from this set? Ultimately I'm using much larger numbers, so simply listing possibilities will not be sufficient.
Thanks in advance.