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

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

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

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 ?

In how many ways can 52 cards be divided among 4 players equally, when (i) each gets equal number of cards? (ii) cards are divided into 4 groups of 14 cards each?

In how many ways can we select a cricket eleven from 17 players in which 5 players can bowl?Each cricket team must include. 2 bowlers.

In how many ways can 52 cards be distributed (i) Equally among 4 players and , (ii) Equally into 4 groups ?

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

In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?

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.

In how many different ways can the first 12 natural numbers be divided into three different groups such that numbers in each group are in A.P.? a. 1 b. 5 c. 6 d. 4