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

Options

A. 36
B. 24
C. 18
D. 20

Answer

D

Explanation

12 others can be divided into 4 equal groups in
`((12!))/((3!))=((12).(11)!)/(6.6.6.6)=((11)!)/(108)`
(18).
`=(10!)/(3!7!)`

`=(12!)/((4!)^(3).3!)`
total ways `=((10)!)/(3!.7!).((12)!)/((4!)^(3).3!)`
`=((12!)/((4!)^(3))).20impliesk=20`