Home
Class 11
MATHS
In how many ways can 7 persons sit aroun...

In how many ways can 7 persons sit around a table so that all shall not have the same neighbours in any two arrangements.

A

720

B

360

C

1440

D

none of these

Text Solution

Verified by Experts

Clearly, 7 persons can sit at a round table in (7-1)!=6! Ways. But in clockwise and anticlockwise arrangments, each person will have the same neighbours.
`:.` Required number of ways `=(1)/(2)(6!)=360`.
Promotional Banner

Topper's Solved these Questions

  • PERMUTATIONS AND COMBINATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|111 Videos

  • PERMUTATIONS AND COMBINATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|9 Videos

  • PARABOLA

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

  • PROBABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|45 Videos

Similar Questions

Explore conceptually related problems

In how many ways can 10 people sit around a table so that all shall not have the same neighbours in any two arrangement ?

In how many ways can 8 people sit around a table?

In how many ways can 8 persons sit in a round table.

In how many ways can 6 persons can be seated at a round table so that all shall not have the same neighbours in any two arrangements?

The number of ways in which four persons be seated at a round table, so that all shall not have the same neighbours in any two arrangements,is

The number of ways in which four persons be seated at a round table, so that all shall not have the same neighbours in any two arrangements,is

The number of ways in which four persons be seated at a round table, so that all shall not have the same neighbours in any two arrangements,is

Statement 1: the number of ways in which n persons can be seated at a round table, so that all shall not have the same neighbours in any two arrangements is (n-1)!//2. Statement 2: number of ways of arranging n different beads in circles is (n-1)!//2.

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.

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.

OBJECTIVE RD SHARMA ENGLISH-PERMUTATIONS AND COMBINATIONS-Chapter Test
  1. In how many ways can 7 persons sit around a table so that all shall no...

    Text Solution

    |

  2. 7 women and 7 men are to sit round a circulartable such that there is ...

    Text Solution

    |

  3. There are (n+1) white and (n+1) black balls, each set numbered 1ton...

    Text Solution

    |

  4. 12 persons are to be arranged to a round table. If two particular pers...

    Text Solution

    |

  5. The number of committees of 5 persons consisting of at least one femal...

    Text Solution

    |

  6. The number of ways in which a team of eleven players can be selected f...

    Text Solution

    |

  7. In a football championship, 153 matches were played. Every two-team pl...

    Text Solution

    |

  8. How many numbers between 5000 and 10,000 can be formed using the digit...

    Text Solution

    |

  9. If x, y and r are positive integers, then ""^(x)C(r)+""^(x)C(r-1)+""^(...

    Text Solution

    |

  10. In how many ways can 5 red and 4 white balls be drawn from a bag conta...

    Text Solution

    |

  11. All the letters of the word 'EAMCET' are arranged in all possible ways...

    Text Solution

    |

  12. There are 10 lamps in a hall. Each one of them can be switched on i...

    Text Solution

    |

  13. How many 10-digit numbers can be formed by using digits 1 and 2

    Text Solution

    |

  14. The straight lines I(1),I(2),I(3) are parallel and lie in the same pla...

    Text Solution

    |

  15. about to only mathematics

    Text Solution

    |

  16. The number of diagonals that can be drawn by joining the vertices of a...

    Text Solution

    |

  17. The sum of the digits in unit place of all the numbers formed with the...

    Text Solution

    |

  18. In an examinations there are three multiple choice questions and each ...

    Text Solution

    |

  19. There are 10 points in a plane, out of these 6 are collinear. If N is ...

    Text Solution

    |

  20. Ramesh has 6 friends. In how many ways can be invite one or more of th...

    Text Solution

    |

  21. If Pm stands for ^m Pm , then prove that: 1+1. P1+2. P2+3. P3++ndotPn=...

    Text Solution

    |