In a knockout tournament `2^(n)` equally skilled players, `S_(1),S_(2),….S_(2n),` are participatingl. In each round, players are divided in pair at random and winner from each pair moves in the next round. If `S_(2)` reaches the semi-final, then the probability that `S_(1)` wins the tournament is 1/84. The value of n equals _______.

In a knockout tournament 2^n equally skilled players; S_1.S_2.......S_(2^n)are participating. In each roundplayers are divided in pair at random and winner from each pair moves in the next round. If S_2 reaches thesemifinal then the probability that S_1 wins the tournament is 1/20. Find the value of 'n'.

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

If S_(n), denotes the sum of n terms of an AP, then the value of (S_(2n)-S_(n)) is equal to

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.

S_(N^(1))and S_(N^(2)) reactions are

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_(3) ,…, S_(16) play in a tournament. Number of ways in which they can be grouped into eight pairs so that S_(1) and S_(2) are in different groups, is equal to