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

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 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.

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

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 ?

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

The probability of ‘n’ independent events are P_(1) , P_(2) , P_(3) ……., P_(n) . Find an expression for probability that at least one of the events will happen.

P_(1), P_(2), P_(3) are altitudes of a triangle ABC from the vertices A, B, C and Delta is the area of the triangle, The value of P_(1)^(-1) + P_(2)^(-1) + P_(3)^(-1) 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,_____.

A system of three polarizers P_(1),P_(2),P_(3) is set up such that pass axis of P_(3) is crossed with respect to that of P_(1) . The pass axis of P_(2) is inclined at 60^(@) to the pass axis of P_(3) . When a beam of unpolarized light of intensity I_(0) is incident on P_(1) , the intensity of light transmitted by the three polarizes is I . The ratio (I_(o)//I) equals (nearly) : a) 5.33 b) 16.00 c) 10.67 d) 1.80