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