Eight players `P_1, P_2, P_3, ...........P_8`, play a knock out tournament. It is known that whenever the players `P_i and P_j`, play, the player `P_i` will win if `i lt j`. Assuming that the players are paired at random in each round, what is the probability that the players `P_4`, reaches the final ?

Answer

(i) `(4)/(36)`.
(ii) 0
(iii) one