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 divided into 4 groups each comprising of 4 players and the best from each group is selected for semifinals then

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

Number of ways in which they can be divided into four equal groups if players $P_{1}, P_{2}, P_{3}$ and $P_{4}$ are in different groups is $\frac{11!}{108}$

Number of ways in which 16 players can be divided into four equal groups is $\frac{35}{54} \prod_{r = 1}^{8} (2 r - 1)$

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, $P_{6}$ is one among them is $20. \frac{12!}{{(4!)}^{3}}$

Number of ways in which 16 players can be divided into four equal groups is $\frac{35}{27} \prod_{r = 1}^{8} (2 r - 1)$

answer is A, B, C.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

1) Number of ways = $\frac{16!}{{(4!)}^{4} 4!} = \frac{2^{8} .8! ∐_{r = 1}^{8} (2 r - 1)}{{(4!)}^{5}} = \frac{35}{27} \prod_{r = 1}^{8} (2 r - 1)$
2) Question Image
3)
To the ways= $= \frac{10!}{3! 7!} . \frac{12!}{{(4!)}^{3} .3!}$