Home
Class 12
MATHS
A class has tree teachers, Mr. X, Ms.Y ...

A class has tree teachers, Mr. `X`, Ms.`Y` and Mrs.`Z` and six students `A`, B`, `C`, `D`, `E`, `F`. Number of ways in which they can be seated in a line of `9` chairs,if between any two teachers there are exactly two students is

A

`18xx6!`

B

`12xx6!`

C

`24xx6!`

D

`6xx6!`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` The possible arrangements of teachers and students can be as follows :
`(i) T S S T S S T S S`
`(ii) S T S S T S S T S`
`(iii) S S T S S T S S T`
Hence, total number of ways `=3*(3!)6!=(18)6!`
Promotional Banner

Topper's Solved these Questions

  • PERMUTATION AND COMBINATION

    CENGAGE|Exercise Multiple Correct Answer|2 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE|Exercise Comprehension|8 Videos

  • PARABOLA

    CENGAGE|Exercise Question Bank|21 Videos

  • PRINCIPLE OF MATHEMATICAL INDUCTION

    CENGAGE|Exercise Exercise|9 Videos

Similar Questions

Explore conceptually related problems

A class has three teachers, Mr. P , Ms. Q, and Mrs. R and six students A,B,C,D,E,F. Number of ways in which they can be seated in a line of 9 chairs, if between any two teachers there are exactly two students, is k !(18), then value ofk is ________.

Number of ways in which 4 students can sit in 7 chair in a row, if there is no empty chair between any two students is :

There are 6 students A,B,C,D,E,F. In how many ways can they be seated in a line so that C and D do not sit together?

Find the number of ways in which six persons can be seated at a round table,so that all shall not have the same neighbours n any two arrangements.

Number of ways in which 11 letters A,B,C,D,E,F,X,X,X,Y, Y can be arranged

There are 6 students A,B,C,D,E,F. In how many ways can a committee of 4 be formed so as to always include C?

A team of four students is to be selected from a total of 12 students.The total number of ways in which the team can be selected such that two particular students refuse to be together and other two particular students wish to be together only is equal to a.220 b.182 c.226 d.none of these

Six teachers and six students have to sit round a circular table such that thereis a teacher between any two students.The number of ways in which they can sit is

CENGAGE-PERMUTATION AND COMBINATION-Question Bank
  1. A class has tree teachers, Mr. X, Ms.Y and Mrs.Z and six students A, ...

    Text Solution

    |

  2. If the number of ways in which a selection of 100 balls can be made ou...

    Text Solution

    |

  3. If the number of circular permutations of 20 letters P, Q, R, S, T , A...

    Text Solution

    |

  4. Let N be the number of points (x, y, z) in space such that x+y+z=12, w...

    Text Solution

    |

  5. On the sides A B, B C, C A of a triangle A B C, 3,4,5 distinct points ...

    Text Solution

    |

  6. The number of ways in which the letters of the word 'LONDON' can be re...

    Text Solution

    |

  7. We have 19 identical gems available with us which are needed 'to be di...

    Text Solution

    |

  8. If ' N ' denotes the number of ways in which 8 different mobilès can b...

    Text Solution

    |

  9. If the number of arrangements of 4 alike apples, 5 alike mangoes, 1 ba...

    Text Solution

    |

  10. Duronto express bound from Jaipur to Mumbai stops at 7 intermediate st...

    Text Solution

    |

  11. There are 6 different balls and 6 different boxes of the colour same a...

    Text Solution

    |

  12. Consider M=2^(4) 3^(4) 5^(2) 7^(2) 11^(2) and number of ways in which ...

    Text Solution

    |

  13. Consider the word 'HALEAKALA'. The number of ways the letters of this ...

    Text Solution

    |

  14. Consider the word 'CARCASSONNE'. Words are formed' using all the lette...

    Text Solution

    |

  15. If (201) ! is divided by 24^(k) then the largest value of k is

    Text Solution

    |

  16. If there are 10 stations on a route and the train has to be stopped at...

    Text Solution

    |

  17. Let A={1,2,3,4] . The number of different ordered pairs (B, C) that ca...

    Text Solution

    |

  18. Number of ways in which three distinct numbers can be selected between...

    Text Solution

    |

  19. Matrices are formed using four given distinct real numbers, taking all...

    Text Solution

    |

  20. If n is a factor of 72 , such that x y=n, then number of ordered pairs...

    Text Solution

    |