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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 toA. `(13!)/((3!)^(4)4!)`B. `(14!)/((3!)^(4)4!)`C. `(6(13!))/((3!)^(4)4!)`D. none |
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Answer» 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!)` |
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