Minor, but no it's 1/(8 choose 4) = 1/70 because there are 4 tea-first, 4 milk-first, and the lady tasting tea knows this. Once the locations of the four tea-f

Minor, but no it's 1/(8 choose 4) = 1/70 because there are 4 tea-first, 4 milk-first, and the lady tasting tea knows this. Once the locations of the four tea-first cups are decided, the locations of the remaining milk-first cups are completely determined. (And there are 8 slots for those first 4 cups, hence 8 choose 4).