Question

Fifteen sudents `S_(1),S_(2),S_(3),….S_(15)`
participate in quiz competition. The number of ways in which they can be grouped into 5 teams of 3 each such that `S_(1) and S_(2)` are in different teams is equal to
A. `(13!)/((3!)^(4)4!)`
B. `(14!)/((3!)^(4)4!)`
C. `(6(13!))/((3!)^(4)4!)`
D. none

Answer 1

C
Required number of ways= (Number of ways in which 15 students can be divided in 5 teams )-( Number of ways when `S_(1) and S_(2)` are in same group )
`=(15!)/((3!)^(5)5!)-(""^(13)C_(1)xx12!)/((3!)^(4)*4!)=(15!)/((3!)^(5)5!)-(13!)/((3!)^(4)4!)((15xx14)/(3!xx5)-(1)/(1))`
`(13!)/((3!)^(4)4!)((14)/(2)-1)=(6(13!))/((3!)^(4)4!)`