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 ?

Eight players P_(1),P_(2),P_(3),............P_(8), play a knock out tourrament.It is known that whenever the players P_(i) and P_(j), play,the player P_(i) will win if i

8 players P_1, P_2, P_3, …, P_8 play a knock out tournament. It is known that all the players are of equal strength. The tournament is held in three rounds where the players are paired at random in each round. If it is given that P_1 wins in the third round. If p be the probability that P_2 loses in second round, then the value of 7p is

Players P_(1),P_(2),P_(3),P_(4) play knock out tournament.It is known that if P_(i), and P_(j) play,then P_(i), will win if i

8n players P_(1),P_(2),P_(3)……..P_(8n) play a knock out tournament. It is known that all the players are of equal strength. The tournament is held in 3 where the players are paired at random in each round. If it is given that P_(1) wins in the third round. Find the probability that P_(2) looses in the second round.

Sixteen players S_(1),S_(2),...,S_(16) play in a tournament.They are divided into eight pairs at random.From each pair a winner is decided on the basis of a game played between the two players of the pair.Assume that all the players are of equal strength.Find the probability that the player S_(1) is among the eight winners.

Sixteen players P_(1),P_(2),P_(3)….., P_(16) play in tournament. If they grouped into eight pair then the probability that P_(4) and P_(9) are in different groups, is equal to