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 _______.

One mapping is selected at random from all mappings of the set S={1,2,3, n} into itself. If the probability that the mapping is one-one is 3/32 , then the value of n

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.

inside the circles x^2+y^2=1 there are three circles of equal radius a tangent to each other and to s the value of a equals 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 decided to the basis of a game played between the two players of the pair. Assume that all the players are of equal strength. (a) Find the prabability that the player S_(1) is among the eight winners. (b) Find the probability that exactly one of the two players S_(1)and S_(2) is among the eight winners.

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

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 three rounds 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 of P_2 loses in the second round.

If S_(n) denotes the sum of n terms of an AP whose common difference is d, the value of S_(n)-2S_(n-1)+S_(n-2) is

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 ?

Let s_(n) denote the sum of first n terms of an A.P. and S_(2n) = 3S_(n) . If S_(3n) = kS_(n) then the value of k is equal to