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 ?

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 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

Thirty-two players ranked 1 to 32 are playing in a knockout tournament. Assume that in every match between any two players the better ranked player wins, the probability that ranked 1 and ranked 2 players are winner and runner up respectively is p, then the value of [2//p] is, where [.] represents the greatest integer function,_____.

Thirty-two players ranked 1 to 32 are playing in a knockout tournament. Assume that in every match between any two players the better ranked player wins, the probability that ranked 1 and ranked 2 players are winner and runner up respectively is p, then the value of [2//p] is, where [.] represents the greatest integer function,_____.

16 players P_1,P_2,P_3,.. P_16 take part in a tennis tounament. Lower suffix player is better han any higher suffix player. These players are to be divided into 4 groups each comprising of 4 players and the best from each group is selected for semifinals .Number ways in which 16 players can be divided into four equal groups , is

2^n players of equal strength are playing a knock out tournament. If they are paired at randomly in all rounds, find out the probability that out of two particular players S_1a n dS_2, exactly one will reach in semi-final (n in N ,ngeq2)dot

2^n players of equal strength are playing a knock out tournament. If they are paired at randomly in all rounds, find out the probability that out of two particular players S_1a n dS_2, exactly one will reach in semi-final (n in N ,ngeq2)dot

5 players of equal strength play one each with each other. P(A)= probability that at least one player wins all matches he (they) play. P(B)= probability that at least one player losses all his (their) matches.

16 players P_(1),P_(2),P_(3),….P_(16) take part in a tennis tournament. Lower suffix player is better than any higher suffix player. These players are to be divided into 4 groups each comprising of 4 players and the best from each group is selected to semifinals. Q. Number of ways in which these 16 players can be divided into four equal groups, such that when the best player is selected from each group P_(6) in one among them is (k)(12!)/((4!)^(3)) the value of k is

Thirty two players ranked 1 to 32 are playing is a knockout tournament. Assume that in every match between any two players, the better ranked player wins the probability that ranked 1 and ranked 2 players are winner and runner up, respectively, is (A) 16/31 (B) 1/2 (C) 17/31 (D) none of these