MathematicsFive boys and three girls are sitting in a row of eight seats. In how many ways can they be seated so that not all the girls sit side by side?

Five boys and three girls are sitting in a row of eight seats. In how many ways can they be seated so that not all the girls sit side by side?


  1. A
    34,000
  2. B
    35,000
  3. C
    36,000
  4. D
    37,000

    Fill Out the Form for Expert Academic Guidance!l



    +91



    Live ClassesBooksTest SeriesSelf Learning



    Verify OTP Code (required)

    I agree to the terms and conditions and privacy policy.

    Solution:

    Given that,
    Total no. of boys is 5.
    Total no. of girls is 3.
    No. of persons to be seated in a row is 8.
    First, we have to calculate the number of ways so that the person can be seated without any restriction is,
    =8! =8×7×6×5×4×3×2×1 =40320  
    Then, the number of arrangements in which all girls sit together is,
    = P 3 3 × P 5 5 × P 6 1 =3!×5!×6 =6×120×6 =36×120 =4320  
    The total number of ways in which all three girls not sit together is,
    =403204320 =36000  
    Hence, the correct option is 3.
     
    Chat on WhatsApp Call Infinity Learn

      Talk to our academic expert!



      +91


      Live ClassesBooksTest SeriesSelf Learning




      Verify OTP Code (required)

      I agree to the terms and conditions and privacy policy.