1. ## circular permutation

hope some body can explain for me for this problem... i already stuck:

In how many different arrangements can 6 gentlemen and 6 ladies sit around a table if no two ladies sit side by side?

ans:
the number of ways in which 6 gentlemen can be seated around a table = (6 - 1)! = 5!.

Then, corresponding to each seating arrangement for the gentlemen, the 6 ladies can be seated in 6! ways.

he required number of arrangements = (5!)(6!)

my opinion is number of ways in which 6 ladies can be seated around a table = 5!.cand not 6!...

any one can eplane why

2. Originally Posted by nikk
In how many different arrangements can 6 gentlemen and 6 ladies sit around a table if no two ladies sit side by side?
ans:
the number of ways in which 6 gentlemen can be seated around a table [in every other set] = (6 - 1)! = 5!.
Then, corresponding to each seating arrangement for the gentlemen, the 6 ladies can be seated in 6! ways.
he required number of arrangements = (5!)(6!)
Once one person is seated, let alone six, it is no longer circular but becomes linear because we now have right and left.
So it is 6!

3. Originally Posted by Plato
Once one person is seated, let alone six, it is no longer circular but becomes linear because we now have right and left.
So it is 6!
tq for the explanation, but why 6 ladies can be seated in 6! ..why is not 5! also as per gentlemen??..that my prob

tq

4. Originally Posted by nikk
but why 6 ladies can be seated in 6! ..why is not 5! also as per gentlemen?
I will try one more time.
If we had n men to seat, then place one of those at any seat.
Now we can seat the others in (n-1)! ways because relative to the first man the table is now ordered (we can seat clockwise from his left or counterclockwise from his right). That is the general rule for all circular arrangement. If we use every other seat and we want to seat n women we have n! ways to do it because that is still ordered by the first man seated.

5. Originally Posted by Plato
If we use every other seat and we want to seat n women we have n! ways to do it because that is still ordered by the first man seated.
yap but we still consider that the women still sit in round table. for that, the general rule for all circular arrangement for the women still (n-1)!???

am i right sir?

i get the question here All about Circular Permutations - TutorVista.com