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
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.
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
thank in advise me