It would be more straightforward to remove the permutations and just display the combinations and the symmetry between heads and tails. And solve it analytically Eg: if p is the probability that the NPC is correct

  P(A|AAAA) = p^4 
  P(A|BBBB) = (1-p)^4

  PMF = (n choose k) * p^k * (1-p)^(n-k)