I believe the answer is wrong in the book and above to the diver question.
Diver one has a 1/5 chance at a perfect dive (4/5 chance not perfect).
Diver two's chance of a perfect dive is not simply 1/5 because he is dependent on diver one not having a perfect dive (so 4/5 times 1/5 = 4/25).
So Diver threes chance at a perfect dive is 4/5 times 21/25 times 1/5 which equals 84/625. Is there something I'm missing?