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Permutation question

  1. Oct 31, 2007 #1


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    1. The problem statement, all variables and given/known data
    6 men and 3 women are arranged in a line
    Find the number of ways:
    A)That they can be arranged without any restrictions
    B)They can line up with no 2 women next to each other

    2. Relevant equations

    3. The attempt at a solution
    A)Well that is simply 9!
    B)This is where it is hard...I thought to find the number of ways that 3 women next to each other could have been arranged and then subtract this from 9!. But then I also have to subtract with 2 women next to each other,but there is a problem if I find this,this accounts for that there could be an instant when there are 3 women next to each other.

    any help on this part?
  2. jcsd
  3. Oct 31, 2007 #2


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    For b), I think I'd do it as follows:
    First choose an order for the men, this gives you 6! possibilities:
    . m . m . m . m . m . m .
    On the dots you can place a woman (but no two, then you would have two next to each other). How many ways are there to distribute 3 women over the seven empty spots?
  4. Oct 31, 2007 #3


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    Well then you can do that 7P3*6!

    but then wouldn't that be very long to write out all of the combinations of M ?
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