Circular Permutation?

  1. Circular Permutation??

    if there are 7 boys and 5 girls, how many circular arrangements are possible if the ladies do not sit adjacent to each other.??
     
  2. jcsd
  3. tiny-tim

    tiny-tim 26,041
    Science Advisor
    Homework Helper

    welcome to pf!

    hi jxta! welcome to PF! :wink:

    Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
     
  4. Re: welcome to pf!

    i think :-

    boys ways;-(7-1)=6!
    now there are 5 girls and 7 seats(in b/w boys) so there are P(7,5) number of ways, the girls can sit.
    p(7,5)=7!/(7-5)!

    i.e, total no. of ways= 6!*p(7,5)
    = 6!*7!/(7-5)!
    = 1814400 (but this ans is wrong).

    ans = 252 (in my book)
     
  5. Re: Circular Permutation??

    you have to divide by 12 (and not 2 * 12 = 24 as you can not mirror) at some step, as it is a circular placement.

    252 is definitely wrong, look at the following (non-circular) configuration:

    B g B g B g B g B g B B

    This gives us 5! * 7! = 604.800 possibilities. Divide by 12 gives 50.400 possibilities. So the answer must be greater than (or equal to) 50.400
     
    Last edited: Nov 25, 2010
  6. Re: Circular Permutation??

    My answer:

    [tex]\frac{( 21 +15) \cdot 5! \cdot 7!}{12} = 1.814.400 [/tex]

    (this equals you answer)
     
    Last edited: Nov 25, 2010
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