# Permutation question

1. Oct 31, 2007

### rock.freak667

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. Oct 31, 2007

### CompuChip

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?

3. Oct 31, 2007

### rock.freak667

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 ?