Hypothesis Tests · Challenge problem

Five subjects’ paired differences are $6, 2, 5, -1, 3$. A randomization test asks: if the treatment did nothing, each difference would be equally likely to have either sign. Among all $2^5 = 32$ sign patterns applied to the sizes $6, 2, 5, 1, 3$, what fraction give a sum at least as large as the observed sum $15$?